I've never had issue with an event being declined, and over the years, I've run some VERY independent, totally unknown/obscure RPG or miniatures rules games. I can only imagine that something might get turned down if there seems to be a logistical issue or if something would go against the basic rules and/or standards of the con.
I know in the first case, when I submitted something for Origins last year that had a glaring logistical issue with how I submitted it (I put the wrong number in for game duration), their events team contacted me to check if that's 'really' what I intended, and we got things fixed. I would assume GC would be the same way.
As much as there is a call for in-demand games, it seems from other posts I've seen over the years, that a variety of games is also desirable. There are plenty of players out there for games (like Dark Heresy) that may not be at the forefront popularity-wise anymore.
Can't speak for rescheduling things, though, since I've never attempted that. I would think that would be possible if you give enough advance notice.