If a purebred dog of breed X mated with a purebred dog of breed Y, both meeting health standards for their breed, is there a better chance the offspring would be healthier than a same breed mating because the gene pool is larger?

In terms of health alone the first answer would be that in breeding two healthy dogs it shouldn't matter if they're the same of different breeds, you're apt to get healthy pups. But this doesn't take into account the question of recessives. Suppose you breed two dogs of different breeds that both have the same incidence of a recessive health problem. The pups would have the same odds of having that health problem as purebred pups of either breed. On the other hand, suppose the two dogs were of breeds that have no recessive health problems in common. This would reduce or eliminate the odds of the puppies of having the health problems of either breed. This is the classic explanation for the theory of first generation hybrid vigour. The resulting pups should not be bred though, since they'd have a good chance of having the recessives from BOTH breeds, so the grandpups would be inclined to be worse off than the purebred offspring of their grandparents. An excellent set of articles dealing with "hybrid vigour" can be found in DogWorld, Jan 1997 by George Padgett DVM.