We've been lucky enough to get to wake Tink up twice. The first time was planned, DH and DD rushed -- walking purposefully, not running -- to Fantasyland for rope drop. (Funny thing, DH had been told about this by someone in line for drinks at Fantasmic the night before. He was all jazzed to do it, and DD was thrilled. DH was disappointed, though, because he thought they were going to wake up a face-character Tink! I had to explain to him that Tink doesn't meet and greet, but I think he's still bitter.)
Anyway, the second time DD and I happened to stroll into Tinkerbell's Treasures about 1.5 hours after MK opened, and asked, not expecting anything at all, but sure enough, no one else had asked that day. Now, this was really off-season, but it just goes to show it never hurts to ask.