Should I let my pets eat corpses?
Yes, let the pets eat!
Pets gain tameness eating. The only time you might not want them to eat (other than the obvious you want the intrinsic) a corpse is when there are other enemies around however I think they'll attack first and eat later.
Sometimes you might want to get rid of a corpse - a troll for example, pets are ideal for this!.
However, pets cannot get intrinsic's by eating - however some are born with them (such as dragons).