I've heard of folks hunting boar with ROAs (Ruger Old Army) revolvers, and while I would want something a bit more potent for any sort of pig (pigs are incredibly tough), I don't see a problem with what you propose ... here's why:
if you're going to kill deer in the woods, the mechanism of their death is usually (but not always) blood loss. If you're shooting a centerfire cartridge, a boatload of tissue is damaged, blood vessels are severed or ruptured, blood pressure drops very suddenly, and the animal looses consciousness and exsanguinates. If you're using a lower velocity (but higher caliber) roundball or conical, you don't get as impressive a wound track, but you get a bigger hole, and pretty much the same thing happens.
To paraphrase the great Elmer Keith, you want to let a lot of air in and a lot of blood out.
Therefore, it is (in my opinion) a mistake to compare the ballistics of muzzle loaders to the ballistics of centerfire weapons. The later relies on creating a boatload of tissue disruption, whereas BP weapons make a bigger hole.
So, is a .54 out of a muzzle loading pistol "enough gun" for a whitetail? I would give this a qualified yes, with the proviso that the shooter does his or her part. [insert tirade about bullet placement here] ... clearly, if you put a 9/16 inch hole through the heart or lungs (or both) of just about any mammal, they're going to shuck off this mortal coil in a pretty big hurry. if you gutshoot the same animal with a 20mm, it will probably take the poor thing hours to die.
mind you, these are the ruminations of one guy ... just my free opinion, and no doubt well worth every penny ...
get close, shoot straight, make little white packages ...
make good smoke!