It is possible- we got it as a 4th fast pass for 4 people in July, and there were actually 3 different times we could select from. However, it never happened again for the rest of the trip, but it did that one day. We have also been lucky enough to score Mine Train as a 4th or 5th pass during spring break as well, so maybe Mickey just feels bad for my bad luck in losing hats and makes up for it in fast passes.
(Edited because grammar is hard.)