I have a friend that put furniture in storage for a winter and found that mice had burrowed in her sofa. I wouldn't think roaches would be a problem unless there is a source of food. But you might get spiders
Just a thought, but I knew someone who had her items stored and things like sofas were "shrink wrapped" by a specialist firm (UK) I would assume you would be able to find a similar company in the US.
We used a storage locker a couple of years ago when we were getting ready to sell our house - we wanted a place to get rid of the clutter we had, old computers, boxes of stuff, etc. so that when the house was shown they could see the house and not the stuff. The locker was clean, cost about $150 for 4 weeks (8 x 10 room) and was useful. When we moved, we just had the moving company swing by there and pick up our stuff.
We didn't have any cockroaches, spiders or other bugs, so if you haven't decided it, I recommend it. Good luck!