As others noted, it is possible. There a few options such as staying at Bonnet Creek which is offsite but surrounded on three sides by Disney property and I-4 on the other. Most people wouldn't even know that you are not on Disney property. You could could stay in the area of Cypress Pointe which is near the downtown hotels and Downtown Disney. You could probably takes Lynx to get to DTD. There is a shuttle service that will pick you up at many resorts but the cost may be more than renting a car depending on the size of the group. I think it was $15 per direction per person and you are at the mercy of their schedule. For one person, this may not be bad as you would pay $11 for parking at the parks so the net additional fee if roughly $18 which is less than the rental of a car but for more than one person, it is a bit expensive where a car rental quickly becomes less expensive.
