Absolutely. But if by chance it ends up being a different hotel, then I wouldn't. I guess I'm unclear on how precise the methods are here... the one time I tried I ended up with a non-Disney hotel (which was fine, but I would have been sad had I been hoping for 60 day FPs or EMH on that trip).
When I search my dates one possibility comes up, but it also says it could be a Hilton or Wyndham with the Dolphin as the third option. It has the $45 fee per night, but then the note says to hurry and "Someone recently got the Hilton Orlando-Bonnet Creek Resort".