On the roll-up doors I have seen (similar to your photo), there are strips of white felt on the back side because the metal skin actually rubs on it's self as it's rolled up, the felt strips are there to keep the metal surfaces from being scratched (painted surface).
However, I would assume the felt rubbing on the surface of a wrap applied to the front of the door would eventually wear through the laminate on the wrap, how long this will take will depend on the amount of times the door(s) are opened and closed.
In my opinion, I think that It wouldn't work out because there will definitely be friction rubbing on the surface of the wrap.