That should be fine. I doubt the staff at the first wing check in entrance will stop you but if they do, just tell them what you said above. So you can check in the parents at the first wing too.

There don't seem to be any detailed checks at the entrance to the first wing, they rarely ask me for my travel class or status as I say hello. The detailed eligibility check is past the check in desks before the security.

You can in practice bring several people with you through the fast track, even if they have no status. Only the lounge entry is strictly policed.