Highly unlikely, and given the fact that McCown has the most experience, I think he should be considered the safest choice to start heading into training camp. Experience usually always trumps in these types of situations, so I think it's going to be McCown's job to lose until either Beck / Henne are able to prove otherwise...
Beck was garbage a year ago, and he certainly has the most to prove. If he doesn't show some significant changes / improvement this season, I think he'll likely end up fading away into nothingness. He's already forced to play catch up considering his age, and nobody is going to want to risk taking a chance on a 30 year old back-up....
As for Henne, {being hand picked by the new regime}, it wouldn't surprise me to see him starting at some point this season. He's the future, and I'm sure that Parcells / Sparano are going to want to see him get some experience before the end of the season....
IN TUNA WE TRUST....