You being in Louisiana is probably not that different from the situation in Florida.
Wild/feral hog 101.
The wild and feral hogs in the south have been here since the Spanish Explorers. The Explorers attempted to carry their pork rations on the hoof. And hogs don't herd so well in an expedition enviroment. Many escaped and being very adaptable, survived. Their descendents still roam Florida and the Southeastern United States. The genetic evidence to support that comes from the mule footed and waddled wild hogs we commonly catch in Florida.
Then add the fact that Florida was a free range state. Meaning folks fenced their crops and left their stock to run wild in the woods. Gathering them at Butchering time. More hogs got loose.
And.... Hunters imported Russian Boars and released them for sport.
Now we have an ustoppable invasive species on our hands. I cannot speak for other states. I know there are populations of wild hogs in most of the Southern States, Texas, California as well as some other states. But Florida tends to be wild Hog Central. I don't think anyone knows how many wild hogs we have in Florida. A million gets thrown out from time to time. But they really don't try to study them. Just control them.
In Florida wild hogs have several statuses. On private land they are the property of the land owner. On Public Hunting Land they are given game status. Mostly to control out of season hunting of other species. (This is changing though because only allowing hunting during deer season does not keep their populations in check. The state is now having off season hog hunts.) On other public lands they are considered pests, nuisances, and general pains. On Federal Land they are also considered pests.
They are VERY prolific. A female can breed by 8 months of age. She will have from 4 to 10 or more pigs and can have two litters a year. Momma pigs are very very good mothers. A crafty bobcat might get a piglet. Panthers get a few piglets as well as young adult pigs. Gators get a few both pigs and adults. Bears get some. A coyote might snatch a baby now and again. Same with the larger hawks and owls. But by an large their survival rate is great. If you watch a litter in the woods you frequent it would be uncommon more than one or two out of a litter of 8 to be missing by the time they are 25 or 30 pounds. And by that time they are home free. The only predators left are bears, humans, panthers, and gators. They are onry and mean by then and can take care of themselves. Before that the mothers are very formidable.
They will eat anything and can survive in places and in numbers you would never imagine. They compete with our native deer, bears, ground feeding birds, squirrels, etc. They eat fruits, nuts, grasses, roots, etc. They will destroy agricultural fields. Sod farms, etc. Plus they will eat ground nesting bird eggs (the birds too if they can catch them) fawns, snakes, turtles, frogs, toads, a weak calf, etc.
Wild hogs have been a part of my life since I could walk. I have a sort of love hate relationship with them. On one hand they have cost my family money and me money personally. They destroy our natural environment and add significant pressure to our native species. On the other hand, they are SMART, tough, tenacious, and great survivors. I admire that.
I grew up in a family that were both hunters and had agricultural operations. So hogs were always both sport and a nuisance. We seemed to always been thinning hogs. I have also been a licensed Nuisance Wildlife trapper since I was about 18 years old....I cannot begin to say how many hogs I have trapped, shot, caught with dogs etc. I have also caught a few in more colorful ways (When I was younger and crazier.) I have bailed off a horse on ones back, bailed out of the back of pickups, off an airboat, etc. Several thousand would be a good safe quess. I have trapped hogs under license in state parks, federal land, private ranches, subdivisions, city parks, farms, even NASA Property and Air Force bases.
Hogs seem to have a mystic or reputation about them as far as being dangerous. They are tenacious and will stand and fight given the right circumstances. And they are capable of hurting you. But I have to say, in all my time, I have never had an unprovoked hog come after me. Provoked ones yes. but then again, I have done a lot of provoking. I have a couple of scars and that is about it. Got gashed on the shin, got bit on the foot (fell down grabbing a hog that was bayed up against a bull panel fence. Was kicking the hog off me) And a slash on one of my calves.
I have hunted hogs with dogs. I have owned hog dogs. I will still hunt with people that run dogs, but I am too tender hearted as far as dogs are concerned to hunt with dogs I have trained and cared for. Because it is a VERY rough game. Hunters do lose dogs.
Basically there are two types of hog dogs. Bay dogs and Catch dogs. Bay dogs bay. Catch doges catch.
Bay dogs can be any number of breeds and crosses. Hounds and curs mostly. Most of the coonhounds, Plotts, etc make good bay dogs. As long as they have a good nose, can run and are fairly fearless. Catahoulas, Blackmouthed, Leopard, Mountain Curs make great bay dogs. Many folks favor the curs over the hounds because they seem to have a bit more grit and courage. Someone mentioned Ridgebacks. I have hunted with a guy that runs Ridgebacks and they do well.
A bay dogs job is to trail, chase and then bay the hogs. Hogs will run when chased by dogs 9 times out of 10. But they will eventually stop. How far they run before they bay up depends on the hogs, the weather, terrain, the dogs, etc. It may be 30 yards, it may be two miles. A momma with pigs is not going far. She is going to find a place to stash her pigs and fight the dogs. young adult sows and little boars will usually run the farthest. Large solo breeding boars will not usually run far. They are tough and know it. They would rather fight it out with the dogs.
When the hog bays up it will be someplace the hog feels he has an advantage. A thicket, Palmettos, ti ti marsh, etc. The hog knows his backside is volunerable so he will find something thick to back up to and make fight from there.
The bay dogs job is not to fight the hog but worry him and get him bayed up in one spot until the hunters and or catch dogs get there. But it does get dicey for bay dogs at times. Hogs depending on age and sex are herd animals. Called Sounders. The big boars are solo or in small groups which is good. But sometimes the bay dogs can find themselves in a thicket with a sounder of hogs (sows, pigs, shoats, and young boars) numbering 30 or more. 10 to 12 is not uncommon. Luckily these sized hogs mostly want to get away. But at times bay dogs find themselves cornered by some tired ticked off hogs and it can be bad.
Some hunters use a second type of dog, and some hunters will dispatch or hand catch the hogs after the bay dogs have done their job.
The Catch Dogs...... These are usually bull breeds and crosses. Pit Bulls and pit mixes are the most common. Some folks use American Bulldogs, Argentinian Dogos, and other exotic Mastiff and bull dog type dogs. But the Pit Bull is the king of this game.
The catch dog does exactly what his name says. He runs in and catches the hog. Some hunters use a single catch dog and some use a pair or even a trio. The dog is smaller and faster than the hog, so he usually grabs him and hangs on. But this is the ROUGH part of the game. It can get ugly. Very ugly. Dogs get cut up and worse at times. In recent years many hunters have gone to using kevlar vests and neck guards on their catch dogs. Which has cut the injuries to the dogs down a bit. That is about as far as I am going with that.
To answer your question..... Having a dog to harrass the hogs is asking for trouble. A herding breed would probably harrass them. But it would have to be a tenacious herding breed. Like an ACD that was willing to run in and bite them to get them going. They actually use ACDs and ACD mixes as both bay and catch dogs in Australia. A Border Collie or other herding breed that herded with looks and eyes would be useless. Because hogs can't see for squat and are not easily intimidated like sheep and dairy cattle. A slower less mobile dog is going to get cut quick and even a fast agile dog is going to get it sooner or later if it harrassing the same sounder of hogs over and over.
They would not leave anyway. They would just pattern you and the dog and become nocturnal.
Your best bet if you want them thinned out is to hire a trapper or find some ole boys that want some pork and let them trap or hunt them.