One important point is that the recoil buffer assembly is IN the stock of the AR-15/M-16. I believe all the Kalashnikov actions have the recoil assembly within the receiver, as Dennis pointed out. If the stock gets broken off of the AK-47 and there is nothing behind the recoil rod/spring. I guess you could fire that gun one more time. But I certainly would not want to be the one firing it!
If you are holding the gun up to use the sights when you fire it, I suspect there is a very good chance you will have the recoil rod sticking right through your cheekbone and possible on through your head. Might be an interesting experiment, but I wouldn't want to try it.
I had a discussion years ago about this problem in reference to the M-16. Grunts used to be able to use the M-14 as an effective club if they happened to run out of ammo. The M-14 was pretty SOLID. The guy said he was told by his drill sergeant that if someone made the mistake us using the M-16 as a club, it would not be possible to fire it after you broke off the stock. I disagreed. I felt that you would be able to fire that gun one more time, but when that bolt carrier flies back into your face, it would certainly ruin your day. I don't know if that gas tube extension on top of the bolt carrier would be enough to stop it's rearwards movement, because I think it would break the charging handle right out of the upper receiver. Again, nothing I want to experiment with to find out for sure......