Yes. Reserve with Alamo at the Car Care Center (location ORLR72). One day ahead of time, call the local Alamo number and let them know when you'd like to be picked up at BLT. I'd say probably a half hour before your reservation starts. They'll send the shuttle...
Don't feel restricted to Alamo. Check with all the major car rental companies for the best price, sine just about all of them have rental offices on WDW property (or nearby). I know that Avis at the Hilton in DTD will send a courtesy shuttle to pick you up if you need that.