Will ceiling junction box support fan mounting?
Mount the fan to the joist or block behind the box, not the box

The two screws in the back of the box in line with the mounting tabs appear to land in a joist or cross-block in the ceiling.  I would attach the fan to that using two 1/4" by 3" structural wood screws (not drywall, deck, or lag screws -- look for something with an ICC-ES or IAPMO rating, such as a FastenMaster TimberLok or Simpson Strong-Drive SDS) through the fan bracket and ceiling finish board into the structural member.