Sure, they would work.....
Over the years I have seen several examples of finely crafted miniature guns. Completely reproduced in every detail.
They would be functional, with ammunition scaled to fit them. The guys who have made these are artists and major modelers. From famous pistols to belf fed machineguns and cannon, all have been reproduced in miniature by some very serious hobbists.
But as far as I know, nobody has ever produced any functional scale ammo for any of them. I'm not sure it is technically possible, and even if it was, the extreme tiny size of the bullets would really limit their effectiveness. After all, its MASS at speed. And that is what makes bullets effective.
As to the legal issues of a micro Tommygun, (for example), I think even the worst fanatic at the ATF would have a hard time getting a prosecutor to take it to court. I see it going something like this...
DA: The defendent manufactured an unregistered fully automatic weapon, if violation of US law!
Defense: The law states a fully automatic weapon fires more than one shot from a single pull of the trigger. (holds up exibit A, in the palm of his hand, and offers it to the DA)
PROOVE IT!
DA: (gaze dropped), stammers uh...um...we were unable to fire the exibit, but his intent is obvious!
Defense: You can't shoot it?
DA: Uh..no..
Defense:Why not?
DA: ...no ammuntion exists for this gun...
Defense: So, it cannot fire more than one round for a single pull of the trigger?
DA: uh, it could....
Defense: Did IT?
DA:...no...
Defense: Move to dismiss on the grounds the item does not meet the legal defintion of machine gun, therefore my client did not violate the law...
If the ATF can get your gun to "fire more than once with a single pull of the trigger", no matter how they do it, they can build a case. Not a good case sometimes, but somthing anyway.
If they cannot get it to do it, even once, they have NOTHING to build a case on.
At least not for manufacturing and posesssing an illegal machinegun.. as to anything else you might have done....in your entire life.......