Our youngest DD will be 2-3/4 when we take our trip in May, and we're not planning on returning to the hotel for naps either. She doesn't generally nap well in carseats or strollers, but is a GREAT sleeper as long as she's horizontal in bed. However, usually she'll get to a point -- especially if I don't push it at all, but just let it happen -- that she WILL fall asleep in a stroller or whatever when she gets tired enough. So, we're hoping that'll work at Disney.
I'm spending the money to rent a very comfy, fully-reclining double jogger while we're there (from A Baby's Best Friend) to increase our odds! And we aren't planning ANY night activities. My girls go to bed early, and I'm not messing with that. Our latest dinner reservation is at 5pm, many are earlier, so most nights we'll be back at the hotel and they can go to bed by 6:30pm. They can then sleep as late as they want in the morning (my guess is 7:30am or so) and hopefully be fresh and ready to go. . .
Good luck!