Yes they do stop in Santiago. Caribe makes two stops and Metro one. You do not have to change buses but do get the chance to stretch your legs, get a drink and use the banos. I would also watch any luggage you placed under neath while the bus bay doors are open.
Caribe tours also makes many unscheduled stops along the route. For this reason we prefer Metro to Caribe as less stops so a slightly shorter trip.
Bob K