Can a speaker falling off the wall kill the tweeter?

Last night, apparently my RTi28 that is in the left surround position decided to fall off the wall, from a height of about 6 feet. This morning, I discovered it on the carpet with the speaker wire hanging out of the wall. When I picked the RTi28 up, the tweeter assembly had popped out of the plastic bracket on the front, so I opened it up with a hex key and popped it back into place. It didn't sound like anything else was rattling inside, so I put it back on the wall, made sure it was secure, and went to work.

Today when I got home, I cranked it up to make sure everything was okay. I ran through the noise tones from my receiver to make sure all was well... except when I get to the tone for the left surround, the tone of the noise doesn't seem to have as much treble as the other 4 RTi28's that I have. There's still SOME highs coming from the tweeter, because passing my hand in front of the tweeter makes those highs go away (meaning it must be working at least partially). I did the same with my other 4 RTi28's and there are definitely more highs coming from them than the speaker that fell. I tried the 5-channel pans on Avia and there is a noticeable tonal difference now.

So tonight, I opened the speaker up again to make sure I hooked the tweeter back up or put it in right. When I opened the grill, the magnet part of the tweeter came off in my hand, exposing the back side of the silk/polymer dome. I looked at the magnet and the small metal part in the middle (with the little piece of foam on it) is touching the side of the other piece of metal surrounding it. Isn't this where the metal ring around the tweeter dome sits to move back and forth? Does this mean the tweeter is shot, or could it be something else?