Does a dweller running around the room with his gun contribute to the attack?

It is hard to tell, but I think it follows the "They are in the room together therefore they are draining each other's health" pretty basically. The first thing that made me think that was when everyone is unarmed. All of them are running around like tools, no one is punching the rad roaches, the rad roaches aren't really biting them either, but everything in the room is getting hurt at a constant drain.

I think it just adds a drain, and the animations are just for our amusement. For example I have a rocket launcher wielding guy, and even before he shoots sometimes the raiders will just fall over because their health was draining by being in the room. It makes sense from a practical point of view, it terms of managing the game play. If they all had hit/miss, needed line of view, proximity, etc...the path finding alone in those 3d rooms would be a nightmare, especially considering how many actors are in a typical combat situation. It would likely, if it worked that way, just make everything "take longer" to resolve which would decrease the play-ability of the game as you would be waiting for ages (already do) for the combat to conclude.

Of course hopefully someone comes in here with some documentation on this. :)

They do contribute to the attack.

Fights in room are a constant drain on HP and are not dependent on the animation.

This can be seen easily with a missile launcher and single room level 1 radroaches incident. The roaches will die before any rockets are fired.