I did not see that they did when I was there in January. None of the DL hotels have a food court so there's really no good place for them to be filled.
The souvenir cups in the park are refillable too. We bought them at the pizza place in CA and got one free refill w/receipt then refills rest of time were cost of regular size soda (they are bigger). Wish we bought them our FIRST day there instead of our third!