Yeah depending on your confidence level and willingness to accept it not being as perfect when you put it back together would dictate the decision to remove it completely. I found when I was pealing it back slightly at driver side door it was not glued as suspected, rather clipped as the other members suggested. And some of these clips are hidden and they clip into roof cross members. The kind of clips that easily break in half if not pulled out correctly. The other thing to keep in mind are the cables that currently run the headliner length. They are fastened to the headliner and can make it challenging to deal with.
Not sure what ways you are trying to run the wires in headliner and assuming you are only doing it to run front to back. I just finished running wires all over that truck. My main pathway was the driver side door jamb channel. All panels are easily removable and wires hide in under carpet or behind plastic panels. If you need to get cable outside in rear, run the wire behind back seat and in channel adjacent to cargo tray, then peal back weather stripping to get it out side. If you are running cables out to front of vehicle via battery or accessories, there is a firewall port on driver side corner very accessible from hood and driver floor board. i just popped it and stuck a philiips through there as to not puncture anything and use it pry space to run wires through.
