Scot, what kind of guitar are you talking about?

Scot-
I'm a novice, and many others on the forum have the experience, data, and expertise to provide good advice.

Nevertheless, I'm going to give you my two cents anyway.

Everything I've read implies that you're trying to work with materials that have a high stiffness to weight ratio, which will generally increase sustain, volume, etc. I'd wager that leather is lower in stiffness, for it's weight, than any suitable guitar wood, and yeah, it's going to damp the sound. Now, if you're trying to do that for some reason, um...ok. But myu guess is that if you're thinking using leather for aesthetic reasons, you'll have some very undesirable results on the acoustics of the guitar.

I remember looking at that D-28 (D-18?) that Presley used to play, encased in a leather cover, and thinking, "man, that's gotta sound like a bag of rocks"

It won't have the same effect on a solid body as an acoustic. I doubt that it will have much of an impact on the sustain, but I'm sure it will color it. But you know there is really only one way to find out. If you pick up a beater at a garage sale, you can use it to experiment on. This could be an interesting experiment. Keep us posted if you decide to have a go at it.