Possible...yes. Probable....maybe. A good planning strategy....no.
Seriously, yes, I have been able to snag even an A&E as a 4th (or more) FP......but it is really and truly the luck of the draw, or an overabundance of pixie dust showered on you. I think the one that shocked me the most was that A&E...and this was back in the height of the 4/5/6 hour lines. I wasn't looking for it, obviously, rarely am for the special ones......but there it was. I pointed at it and both my daughters said, at exactly the same time: "Nahhh, that's gotta be a glitch".....we grabbed it and it was for real.
If you are really hoping for something lucky like this though...plan to stop at any FP Kiosk within a quarter mile of your present location....and check it often, and then some more. Someone somewhere has been kind enough to change their selection to something less important so that YOU can have that great unexpected FP.....grab it first, and THEN raise your eyes to the heavens and thank them.