They take that medical issues VERY very seriously here at UPS and a back problem would probably be a situation that would need to be considered greatly, given the nature of the jobs, from the context that you are speaking. You would have to have a doctors note stating your issue with clearance and they would still determine if you'd be able to work. Given that the proper lifting and lowering methods, which the company reasonably pounds into your head, emphasizes itself on preventing back injury (which is very much a real risk) and other injuries, it sounds like you would especially be closely looked at.
A chick who I got hired on with the first time I worked here had a pre-existing hand issue informed her PT sup about it, and even though she had a sufficient aid, they let her go not a full two weeks after she was hired because she couldn't get an evaluation/doctor's note in a timely fashion. It was probably a good decision for her, too.
Like I said, they take the risks seriously and you don't want to risk it either. Been through the process myself once. It's a REAL pain in the ass, from being hurt to the actual injury reporting, and even the follow ups they do on you. Oh and then somehow you get ostracized by co-workers who are
because you caused them to lose out on pizza -_- It sucks. Just let them know. You won't regret it, the worst case scenario, you go and look for another job.