As a PP said, yes you can! Here's a few details:
The
Alamo location code for the Car Care Center, which is attached to the Hess station you pass as you leave the Magic Kingdom, is ORLR72. The Alamo location for the Dolphin is ORLR74.
What you do is make your reservation online, as you normally would, using the location codes above. You can also pickup/dropoff at one of those locations and dropoff/pickup at MCO, if you wish. The cost is usually the same for doing that, but not always.
If you are picking up at the CCC, you call the local Alamo number at the CCC the day before you want to rent the car and tell them when you would like to be picked up (probably about a half hour before your reservation starts) and they'll pick you up at your resort and take you to the CCC. (I'm not sure if the Dolphin has the shuttle, but there's other ways to get to the Dolphin anyway -- like walking thru Epcot, among others).
If you return the car to the CCC, my experience has been that they'll drop you off at the Kennel Club (sounds funny, but its at the Ticket and Transportation Center and you can get pretty much anywhere from there). I've heard others say they'll take you other places, but maybe that depends on if they're going to that resort to get someone else.