Convertible doors have, I think, one extra piece of reinforcement added that t-top doors don't (won't hurt anything), and the two have different glass. If you swap the glass, they should be interchangeable.
'83-'86 and '87-'88 doors vary in a couple of ways though: the '87 and newer doors have a factory speaker in the lower front corner, and the bottom mount window channel is anchored in a slightly different location. Some modification might be necessary there to use an early model door with a later model door panel/interior. I saw a write-up somewhere online a few months back of someone modifying the doors on an earlier model car to accept speakers in the later-model factory location, including relocating the bottom mount of the window run channel, but don't have a link handy. I had been searching for something related to door speaker installation in an '84-'86 Mustang when I ran across it, I think, or maybe something about T-top weatherstrip installation/window adjustment.
This forum (dedicated to "four-eyed" Fox cars) has some info on what parts are needed for door conversion, etc. (Maybe some other relevant threads too if you search for "roof").