I have done it
I can tell you that I have just successfully put a 3gs battery, and logic board into basically a 3g frame. The reason for doing this was that the 3gs was dropped a few times leaving the lock button almost shot. Also the metal rim of the 3gs was coming apart and causing some problems. Then some other weird stuff started happening. So I decided to try to take the logic board and battery out of the 3gs and put them into the 3g.
Now, to do this take out the logic board and pull out the battery and the sync port (search youtube for some "how to" vids). Then, simply pull the same parts out of the 3g along with the camera(the camera will not work so just take it out to save you the trouble, also I heard it wouldn't work anyways because of software mismatch but I didn't try it I just took the whole camera out). Then it's a matter of just replacing parts. Firmly press the 3gs battery back into place in the 3g shell, then replace the sync port and logic board. Also, I forgot to mention you need to keep the whole 3gs screen assembly (glass digitizer and all) to put into the 3g shell, sry bout that, but it fits right in the 3g. Then simply reconnect all the connectors and place the screen back on and screw it in. That's it. And everything works just like the 3gs but in a 3g "body" even the headphone jack is compatible so you dont have to replace it. Just the battery, logic board, and screen.