I have no doubt that should a great GM Candidate exist, and be hired, and NOT want Rex, that GM would be given permission by Woody to fire Rex.
Just because Woody says Rex isn't going right now, doesn't mean thats all she wrote. New GM hired changes everything, and Woody can always say "well, my great new GM wanted to go in another direction".
Tanny gone/Rex staying also lays squarely the blame for the Sanchez pick (worst QB in last 4 years) and Tebow aquisition on Tannenbaum.
Best of luck to him in his next job (cause he will get another GM job IMO).