Coke Corner is also the only one who will refill their cups, so...yes. Also, some of their employees are not aware of this (most are but heard a couple friends in November that had a bad experience with one who didn't and laughed at them.)
The coffee shop - not sure about refills (BUT, as I am a Starbucks junkie and have a major problem with the coffee quality elsewhere), the coffee shop on the way from DLH to DL, first stop as you walk into DTD, right next to Starabilla's - looks like a book shop, think it's called Compass Books. That is the best coffee I've found in the entire resort. Now, I can't drink straight coffee. I like my peppermint mochas. DO NOT get coffee at the place by Goofy's Kitchen if you are picky about your coffee, it's the most bitter stuff I've ever had.