There are almost always too many teams starved at QB for one or both of them to fall to 12. There are currently 4 teams ahead of pick 12 that need QB's for sure (Houston, Carolina, Denver, Washington), and another 2 that could possibly pull the trigger if they fall in love with a certain guy, but will probably have to wait at least one more year based on their current QB contract (Detroit, Atlanta). That doesn't include trades. Jacksonville and Detroit could trade away their pick since they probably won't use it on a QB and get a bunch more picks.
With that said, if Pickett or Corral "fall" to 12, I'd be all over that. If it doesn't work out, get rid of him and try again in a few years. Honestly, I wouldn't touch the Liberty kid. He might be amazing, just don't know that I'd blow a top 12 pick on a QB from a place like Liberty, right or wrong. I've said it before, but QB is just too important in the current day NFL - keep swinging on QB's until you find one. If Pickett and Corral are gone, I'd take Linderbaum, assuming he's still available. Bradbury is terrible and needs to go.