It all depends on how Garrett is perceived in the locker room. Guys who don't really like Garrett or are indifferent may react as you describe. But players who really do like Garrett will likely fight and play harder for him. Jason Witten said when it was announced that Garrett was staying said he was happy about that and essentially that the guys in the locker room would do anything for Garrett. If this is true, then having Garrett in the last year of his deal may be a motivating factor for the players. But since we aren't in the locker room, how the players will react to Garrett's contract status is anybody's guess.