Unless you are either a lock for the 1st round or an attention whore, I think it's a mistake to be in the green room. If nobody picks you in the 1st round, you wind up looking like a loser on national TV. It was different back in the days when the 2nd round began immediately after the 1st round ended, or even farther back before the draft became a made-for-TV event. Nowadays there just seems to be more downside than upside. Ultimately, where you decide to be on Draft Day won't have any impact on your success (or lack thereof) as an NFL player, but neither does a kick to the nuts - you'd still like to avoid it if you can.
I think Kizer should watch the draft at home with his family like Clausen and Manti did.