In my experience, the kind of people I'd be willing to allow to 'board and train' my dogs don't actually call their services 'board and train'. I'd still personally need an existing relationship and significant level of trust with someone before I let them take my dog and work with them without me in their home or facility, and there's only a few circumstances I could see that kind of setup being more beneficial than anything I could do at home. General good manners aren't on that list, because as others have mentioned, many dogs don't generalize 'I behave this way in X space' to 'I also behave this way at home'. Or even 'I respond immediately to X command when person A says it' to 'I respond immediately to X command when my owner says it'.
Puppy raising is a little different, where the puppy raiser will likely have already started on some fundamental manners training and foundational behaviors for a good house dog (or sports dog, or service dog prospect, depending on the situation). But a good puppy raiser focuses mainly on socialization and helping the pup develop into a stable, confident dog, and doesn't guarantee to the puppy's owner that they're now 'fully trained' and need no further work, ever. But that's not something you see much outside of certain service/working dog communities, or occasionally with sports dogs.
I'm rambling. Basically, most board and train facilities make their money on being able to hand over 'fixed' dogs after a relatively short amount of time, and promising the owners they have to do little or nothing to maintain the new behavior. Sadly, one of the best ways to achieve a dog that doesn't show 'bad' behaviors is to make it so scared to behave at all outside of direct commands that it basically acts like a lump the rest of the time. And also sadly, many dog owners see this as a good thing because they don't understand why their dog is acting this way. While I'm sure there are a few board and train facilities out there that don't take the 'by any means necessary' approach to getting results, it's so prevalent that I wouldn't risk it with my dogs.
I agree that a boarding place that does some training sessions as fun mental enrichment during your dog's stay would be a better bet, though definitely still vet them thoroughly in regards to what kind of techniques they use. And LeoRose is also absolutely right - in the US, ESAs do not need any specific special training, since they don't have public access rights beyond what a pet dog has.