When a cow gives birth to a stillborn calf will she breed back quicker than if she had given birth to a healthy calf?

Yes. Interestingly, this is a good example of how dairy cows come back into heat sooner than beef cows. Dairy cows that do not have a calf suckling on them (even though they are producing more than twice the amount of milk), actually come back into heat sooner than beef cows. Research has shown that this is because the calf actually inhibits ovulation. If calves are taken off their dams early, (like, 30 to 60 days after birth), the cows will almost always resume cycling much more quickly than if they were raising a calf.

All in all, the simple explanation to the question above is this: A cow that gives birth to a stillborn calf (or has aborted early, or has been weaned early) comes back into heat quicker because partly she's not being suckled, and partly because she will dry up (if she isn't made into a surrogate mother for an orphaned calf), resulting in the decreased drain of energy reserves on her body. Hence, she can put those reserves into returning to her normal estrous cycle instead of growing a calf.