I'm sure he thinks so, but in reality there's no way he competes for the starting job. Chan and Buddy are both known to be straight shooters. They don't play games with this kind of thing, ala the Tebow signing for the Jests. If Gailey and Nix say he's competing to be the backup, that's what he's competing for.
Now if VY makes the team ahead of Thigpen, and Fitz gets hurt, and VY needs to play for an extended number of games and lights it up like Brady when he came in for Bledsoe, we've got a wonderful problem on our hands.
I don't see Fitz getting benched because of bad play. He's the starting QB, and won't play bad enough for that to happen. In the 2nd half of the year last year, he clearly wasn't lights out like he was in the first part of the season, but he certainly wasn't bad enough to be benched. It was clearly his team, and Fitz is the leader. VY can't hold a candle to Fitz when it comes to that.