Theoretically yes, but ingame, not so much, lol
This comment is kinda baffling to me. Because you do have SIZE categories and VOLUME categories. All units clearly declare both of these factors in their combat classes.
Regardless of the size of the dogs in the unit, as variable by breeds (unless you're trying to include such behemoths as Great Danes) the SIZE category of the unit is small (thus height at normal resting stance is around half that of an average human and the length of the body is at or less than the height of an average human.)
Thus if we want groups of particular BREEDS of dogs, then we should create new dog unit templates for those. You could certainly have a unit of Chihuahuas that would be a Tiny sized unit and potentially able to thus benefit from that small size and yet similar strength by taking sting promos. (That'd be kinda cool for a special unit

) And you could have Medium size dogs (from really big breed stock) from much the same thinking. But the current definition of a dog is based mostly on your standard German Shepherd, hip height. And the Felines are Medium sized based on your standard Jaguar - Tiger - Lion size (Human or a little larger body mass.)
Merging never ever indicates a change of size,
only group volume.
I'd love to let canines merge and split but when you get to upgrading to an LE unit, it's exploitable to allow it. Why? Because just before upgrading your dogs, you can split them all down to solo group size, getting tons of them, then upgrade them, and each one of those now thousands of dogs gets the same amount of crime control as the standard group size and each of them are also costing so much less for upkeep due to the smaller group size. So you can get a massive amount of cheap crime control this way.
It's also got an issue with Canines being a vision specialty unit. This would mean you could train one, split the unit, and support 3 cities with one unit to cover the visibility needs the dog fills in for. Not really intended. You'll notice most other vision specialist units are also incapable of merging/splitting, in part for this reason.
As for the cats, they operate a lot like strike teams and allowing them to merge thus REALLY makes them WAY too ultra-lethal and uncounterable. This is particularly true since only they would be able to counter themselves at that point but only one nation can ever get them. I suppose it certainly makes a case for those really strong master big game hunters... but yeah, I think too strong to allow it when all other black ops style units cannot merge or split to keep them from overpowering heavily merged military regulars too easily.