Actual rocket scientist here. I worked at Marshall Space Flight Center, on Redstone Arsenal. Specifically I was working on external aerodynamics on the Space Shuttle External Tank. I also specialize in thermodynamics.
Your guy is full of crap.
As others have said, this is a simple First Law problem. You can't get energy from nothing.
Interestingly enough, if you were to make a ring-shaped bullet, with an internal profile similar to a pair of airfoils (quickly narrowing, then slowly expanding), then put a solid fuel inside, you would effectively have a solid fuel ramjet. That could actually work. Perhaps you missed the part about the solid fuel?
But there is no way for compression to heat the air to a plasma, not short of something like re-entry velocity. Smokeless powder firearms are incapable of generating that kind of velocity. Only light gas guns (they use compressed hydrogen:
http://en.wikipedia.org/wiki/Light_gas_gun) can get that kind of velocity. And if a bullet was able to do that, it would spend its kinetic energy (speed) in order to do so. That little plug of plasma inside the bullet would push equally on the front and on the back of the bullet to get out - there would be no net force except for drag.
I saw a "science experiment" way back in high school (that was last millennium) where someone built a ramp and two wooden blocks with wheels. Both blocks had holes straight through them - one was a straight hole, the other had a constricting then expanding hole. He rolled them both down the ramp, and the one with the constriction went a few inches farther. He said basically what your guy was telling you - the forward motion compressed the air, which then expanded in the second section and provided thrust. Even in high school, I knew he was full of crap. How he made it to the state level science fair, I don't know. Probably stupid judges (they literally pull them off the street for every level of science fair up until state).
