Yes, we take ME to/from the resort--really nice. The past few years we have been at BWV or BCV so getting to the Dolphin was a quick walk. We do a split stay so when we dropped it off, we ended up heading over to Epcot, walking around for a bit, and then headed back to BLT where we were staying for the end of the trip.
We pick up Day 2 and drop off the day before we leave. It works great since we really want the car for the day we switch resorts, to visit AK, and to go to DTD.
I have heard that the Car Care Center will pick you up but have not used them. I believe that you can rent from both ALamo and National this way.