Like all things related to tipping, this is really a personal decision.
That said, I've never tipped. (I rarely utilize the pick-up service since my local branch never shows up when they promise to...but I usually have them drop me off when I'm returning the car).
A tip when you get picked up may be viewed as a bribe for a free upgrade. This may or may not work in your favor. That said, the driver is rarely the same person (IME) who works at the counter, so it would probably be a waste of money to tip for an upgrade.
Also, in 8 years of using Enterprise, not a single driver has offered to help me with my bags. I assume this is a policy for liability reasons (and frankly I don't want or need them to help me). But that reduces the "obligation" for a tip in my mind.
For all I know, Enterprise doesn't allow its employees to accept tips. But maybe they do. In any case, the basic answer to your question is, no, you are not "expected" to tip for this service.