Since they do have Coffee Makers in the Suites which would mean they have "extras" for replacement purposes,if you stay in a non-suite,you could give it a shot and they may "pixie dust" you with one,but I DEFINITELY would not count on it.
However,I did read a report from a Little Mermaid(non-suite section) Guest at Art of Animation who went to the Front Desk at AoA and asked for one and their request was granted,so it does happen.
Over the next couple of years,all of the All-Star Resort will be refurbed and the refurb includes Coffee Makers.