I’m of the mind…You snooze you lose. They waited to join and now they have to deal. They can tag along, and see if it’s truly ‘booked’ but they better not be shocked if they can’t get in.
I served in a tight restaurant and it was a pain in the tuckus when a party added more people than originally planned, especially if the table(s) were already packed. It ruins the whole dining experience imo to have people tripping over extra chairs around me.
PLUS…you have NO idea where they’d seat you and for all you know there could be a table w/ a highchair, stroller, wheelchair, etc near you making it all that more tight and smooshed.