I would say it will depend on how long you will have to store them that way.
8 years ago we moved north after 35 years in our home in Virginia. We moved ourselves so I did all the packing. Our old home was sold in January and when we arrived at our new home which was not finished everything we owned ended up if 3 rental storage units for over 5 months. I used large plastic tubs with locking lids and some of the tubs I bought also had wheels. Everything was fine even after the prolonged storage.