I don't think so. You can expect Henne to make the same kind of mistakes John made his Rookie year and then some. John is a much more polished passer. The only thing Chad has on John is size (and not much). John has everything else.
I fail to see how playing with a familiar QB helps a lineman play better. It seems like you either block your man or you don't. You never see who's behind you or what he's doing so what's the diff? Maybe playing with fellow OL.
John is basically in the driver seat here. He's been in the system the longest (even if that system has changed), he's got the support of most if not all of his teammates (or those that are left), and it's not lost on the organization how hard he works. I would expect to see their faith in him strengthened as the offseason and camps start up. This is the NFL, they're not going to not play the best QB they have on roster. If that's not John come opening day, then it's nobody's fault but his own.
. But I find it hard to interpret as a vote of confidence for John Beck. I think the team could be improved more by filling line holes or a WR, or a DB, or well, anything. Either that or Parcells believes the QB is just as much of a weakness. Which it probably is.