There's a lot of classical behavior research on the phenomenon of imprinting in animals, and I think a sort of weak imprinting could happen with dogs as well. It seems plausible to me that dogs would tend to gravitate toward other dogs that look like the milk bar and like their siblings and that the tendency could carry over to some extent into adulthood. It would be interesting to see if puppies raised in a puppy mill where they might be surrounded by cages of other dogs that look very different from their mom, and where puppies might be taken away from mom sooner, would show as strong a preference for their own breed as puppies raised with mom and siblings and not exposed to other breeds until they were older. I'm just totally hypothesizing here, but I think it's an interesting question.
One anecdote that sort of goes along with this idea of imprinting occurred in our tracking group. At the time we had five or six shelties in the tracking group, and they all happened to be tri-colors (ie mostly black and white). A new member showed up for practice with her sable sheltie who just happened to come from a sable mom and had all sable litter mates. The sheltie was about a year old at the time, very very well socialized with all kinds of dogs. As per tradition, at the end of practice we turned all the dogs loose to play. So there were a half dozen black and white shelties, a black and white border collie, a black lab, a black schnauzer, a couple tri color collies, and the sable sheltie, and a blond cocker. The cocker and t he sheltie just stuck to each other like glue. Everyone in the group commented on the color segregation. So, my hypothesis is that both of these dogs had at least loosely imprinted on brown as part of their recognition, and that in that sea of black and white dogs, the color attraction overrode recognition based on head and body shape and behavior and other features. Just a guess, but it was hilarious to see these two little brown dogs instantly become best buddies amidst the mass of other dogs.
But, while I think there might be a recognition and affinity for dogs of different breeds, I don't think that it matters a bit when deciding about having two dogs living together. I think the individual personalities of the dogs far overrides any recognition they might have for their own breed. If dogs can learn to co-exist peacefully and even amiably with cats, birds, bunnies, etc I wouldn't give a second thought to whether a basset and a border collie, or whatever combination, can become buds. If they have the personality to get along with other animals they will do just fine, and if they don't have the personality to get along with other animals, choosing the same breed won't help."