I don't see why you couldn't, make sure you have a couple of electrical outlets and I would do a very thorough scrubbing first.
Some LQS and some chains even do have "Sew Suites" often with a machine, some have a price attached others are free but no storage for your stuff.
I don't have issues with bugs where I live so I store my fabric in cardboard boxes but you never ever want to put cardboard (especially cardboard full of fabric) directly on the concrete. Moisture will wick in and you will get the musty smell. At the very least, put down a couple of 2x4s and rest the boxes on top of that and make sure the back of the boxes aren't touching the walls either. I have a couple of rolling wire storage racks from Costco that my boxes are placed on.