Depends on what they did instead.
If the Mayor had his way, probably have Willow turned into a vampire minion in revenge, and to learn what Willow knew of the box. (Hopefully she'd be saved before that.) Come to think of it, a vampire was going to take "just a taste" which could've easily become more given vampire discipline (the one taken down by a pencil).
Beyond that, I'd think the mayor would pull all stops, using deceptive magic as memory spells in addition to special demons. Maybe even the Order of Taraka. The box was too important and he had limited time. It's just who knows who else (and why) would be interested in the box for themselves.
If he thought it was about to be destroyed then he'd go in immediately. Even just backed by Faith he could do a total party kill on Buffy and all the Scoobies. And enough others had been killed at the school (can't forget the wasps during the haunting) without a fuss raised over it, even if Buffy got a special Class Protector Award soon after. Snyder and at least one cop knew the truth but covered it up. All in all, doom.