I haven't had a 3 legged basset, but I have had a 3 legged lab mix. He lost a front leg and recovered just fine. He was still able to run, catch frisbees, and even swim a bit.
In the case of a basset, I think it would be easier if he's of lighter build. Also, a rear leg would probably be easier to deal with than a front. If your vet thinks he can manage okay I say go for it.