probably not. The new vettes are unibodies, which means there is no "chassis" but a perimeter structure that is throughout the car. The second problem is that a vette is bound to be a bit different in its track width and wheelbase.
I'm not saying it can't be done, just that it wont be as easy as bolting the Firebird body on top. Which is also a unibody, so you would have to cut it up a bit just to drop it onto a chassis.