So are you saying that with a rimfire action it is possible to release the hammer before the bolt is fully in battery...? Because it seems like that's what you're saying...
Yes it can, on both the 22 and the rim fire versions of the AR. It is easy to demonstrate with a full-bore AR but I haven't tried it with a 22.
The hammer can release before the bolt is fully closed, in the 223 this will mean it won't fire, in the 22lr version it means it could fire the round. I have witness someone firing rapidly with a 22AR and the rounds were regularly going off before the bolt had full closed, there was a lot of flash and brass bits coming out of the eject port and still it reloaded OK.
It is the use of forward assist on a rim fire round that I wouldn't advise. If you are having trouble with the bolt closing on a rim fire and take a look to see why the rifle failed to fire, if the bolt is half way back then the round most likely is bent and should be discarded as a damaged - I would also not advise attempting to shoot a damaged round.
If the bolt has ridden up over the rim then forward assist will damage the round further.
If the bullet is still in the mag and the bolt has stopped on the rim I would not advise the forward assist in this instance as it could fire the round.
Similarly if the bolt is almost home and failed to fire then the hammer has fallen, forward assist now will not work, and, depending upon the cause of the round failing to fully chamber, it could go off if attempting to force it home.
Personally if a round fails to chamber I would try to find out why and in so doing the bolt is pulled back. If it is a failure to fire then as a shooter I would have already assumed the bolt to be fully home otherwise I wouldn't have tried to fire in the first place, then perform your drills and fire on.
As someone mentioned earlier, if on a timed stage and a round fails to fire, the quickest and most likely action to take to remedy the situation is to manually cycle the action watching to see if a round clears and a new one chambers, then continue with the CoF.
Otherwise you are likely to waste more time. If the round fails to fire as sometimes happens forward assist won't help, if the round failed to fully chamber and the hammer has fallen forward assist will not help, if you are out of rounds forward assist will not help. The only situation I can think of where a failure to fire that a forward assist may help is if the bolt has not moved forward enough so that the disconnecter still has the hammer. However manually cycling the bolt and checking that a round chambers will solve the problem every time.
(If the firing pin has broken or there is another mechanical malfunction, that is another issue altogether and the forward assist won't help.)
In all instances the manual cycle of the bolt and checking of the chamber/bolt configuration will solve the problem or show up an issue needing a closer inspection, forward assist may only help in the vast minority of the cases. If I was a numbers man and playing for score then I would not use the forward assist method but the manual/check method.
I advise anyone not to use the forward assist on a 22lr round - I have seen a rim fire round go off in just this situation.
Others may say it is OK.
You chose how you want to proceed.