They can refuse the exchange if you show up after the inspection expiration date of the tank -- so there's time pressure to use it.
I had that happen to me. I had exchanged a one year old tank, then the next refill they refused to take the tank I had received in an exchange.
If you do tank exchange make sure the expiration date is at least a few years in the future, unless you know you're going to use it soon.
BTW -- U-Haul (in larger hub locations) does fill your tank. So do most places that sell wholesale compressed gas. If you have an aluminum or fiberglass tank you'll need a refill.