You'd only be able to pull the side panels. The bumpers would have to stay.
I'll bet the fender flares go down to the bottom of the body behind the front wheel opening and in front of the rear wheel opening. It looks like the trim is cut around the flares in those spots.
I'd probably leave the rocker trim on.
It might look okay, but then there's the holes or rivets to deal with.
Unless you're planning on painting anytime soon, I'd leave all the trim on...
I vote either way - but with the caveat that the work may not be worth the effort.
If you're going to take it off to check for rust, that'd be a good time to snap some pics and take a real good look at the different combos.