3200s were out of production before Remington offered choke tubes period. Triggers are mechanical as far as I know. Shouldn't have any problem with chokes, you'll probably have to have thinwalls put in (Briley would most likely be the go-to company for this), but there shouldn't be a problem.
I would forget about installing chokes in the 3200. The barrels are thin and not the best candidate, even for the Briley Thin Walls. Some barrels may have a little more meat, but you take the chance of ruining a good set of barrels.
The Remington 3200 has mechanical triggers, work great. They were produced far too early to have factory choke tubes. but Briley thinwall chokes can be installed easily. I had my 3200 set up with Briley thinwalls sometime back. They have worked without a problem, as long as you check regularly to see they are fully seated/tight before a firing session. The thinwalls do seem to be able to work loose a bit easier than some (some of my Berettas with factory chokes also do this) but checking and tightening before a round takes care of that. I would say go for it.