can anyone tell me if I can install a ceiling fan with this box? It is drilled directly into the stud
You have an entire fan canopy. There is plenty of room, IMO.With your configuration I would recommend a saddle box that is fan rated. Some localities don't allow pancake boxes due to space limitations for wires.
My concern was "through" wiring that would exceed the pancake box's capacity. The saddle box takes care of that problem. He doesn't appear to have any , it is a moot point. Pancake away!!There is plenty of room, IMO.