Naches may or may not chase your cats. If he chased one in foster, he is likely to chase one in your home unless you have super confident cats who stand their ground and do not run. How a dog is with toys and how much they bark are not necessarily indicative of how much prey drive they have or how they treat cats. The most useful information would be how he treated cats in his previous home, if he has known history.
Regardless, I would recommend preparing for the worst and setting boundaries from the start. If his cone makes it hard for him to be kennel trained (it's not impossible, it is just a hassle and requires a large enough kennel), you might look into using an exercise pen or gates instead. Also, they make inflatable neck pillow type 'cones' these days that prevent a dog from licking certain areas but allows a lot more range of motion, such as eating out of a bowl comfortably and eating out of a Kong. You might look into that.
But the bottom line is, unless your cats are super confident and Naches is respectful of cats to begin with, you might be looking at months of adjustment. Prevent ANY chasing from happening. Make sure your cats have comfortable hiding spots and tall places, or maybe even prevent Naches from entering a certain room that is the cats' favorite. On the flipside, teach Naches where he is allowed to be and reward any calm behavior around the cats. When there are animal dynamics to work out in a household, I never allow the new dog free reign and instead restrict them to a small area where they 'live', and they are allowed in the greater area only under supervision, on a leash, and when training/settling directly with me. It is much easier to prevent mistakes, accidents, and habit forming. It is harder to restrict a dog after it has already experienced greater household freedom and it is harder to train after they've discovered chasing is fun.
Regardless, I would recommend preparing for the worst and setting boundaries from the start. If his cone makes it hard for him to be kennel trained (it's not impossible, it is just a hassle and requires a large enough kennel), you might look into using an exercise pen or gates instead. Also, they make inflatable neck pillow type 'cones' these days that prevent a dog from licking certain areas but allows a lot more range of motion, such as eating out of a bowl comfortably and eating out of a Kong. You might look into that.
But the bottom line is, unless your cats are super confident and Naches is respectful of cats to begin with, you might be looking at months of adjustment. Prevent ANY chasing from happening. Make sure your cats have comfortable hiding spots and tall places, or maybe even prevent Naches from entering a certain room that is the cats' favorite. On the flipside, teach Naches where he is allowed to be and reward any calm behavior around the cats. When there are animal dynamics to work out in a household, I never allow the new dog free reign and instead restrict them to a small area where they 'live', and they are allowed in the greater area only under supervision, on a leash, and when training/settling directly with me. It is much easier to prevent mistakes, accidents, and habit forming. It is harder to restrict a dog after it has already experienced greater household freedom and it is harder to train after they've discovered chasing is fun.