Is it possible for the doors on an f-150 to become misaligned after the airbags deployed. I don't think this was caused by the accident since the only damage to the front of my truck was a bent license plate bracket.

 

With deployed airbags you took a lick that could have bent the frame and cause door alignment problems.

 

I would agree, when I had someone turn in front of me and hit them the air bags did not deploy BUT the front fenders warped slightly and the cab was dislodged a bit.

 

So let me see if I have this right, the Honda Civic I rear-ended bent the frame of my four thousand pound Ford F-150?

 

Possibly.
You can also bend your frame on poles, trees, rocks, pretty much anything on and off the road.

Sensors for the airbags aren't behind your license plate frame, it's lies on the frame rails or restraints control module. You probably have more than just a bent license plate.