How many extra guests are we talking about? There's no way for Disney to block the public path that goes by Luau Beach, and I have heard of past Memories events having a few extra onlookers. But Disney's not going to like it if 25 extra people just "happen" to be standing around the beach during your ceremony because they specifically designed this package to be small and easy to manage.
If you do decide to have a private ceremony and only invite guests to your reception meal, you may find that people are very understanding about the guest limit and just happy to celebrate at Ohana with you. ...Or you may get some who have their feelings hurt. It's hard to say. But if, like you pointed out, the main attraction of the trip to your guests is celebrating birthdays, they might not mind.