Again... It's been done
here.
The problem is that you can only effectively air cool a pelt that's no more than 80 Watts, and that's insufficient for today's CPU (the rating isn't comparable to the CPU power). You could get away with 2 * 80W pelts, both aircooled...
The clamping pressure on the Pelt is critical:
OnDaEdg's article.
Fins/heatsinks are going to be important, on both sides. Keeping it all sealed might be a challenge, in the long run.
Energy consumption will become a factor.
Otherwise, it's a pretty cool thing to build