Is it safe to super glue a broken fan connector back to the logic board?

Epoxy and\or super glue may be very effective at gluing the connector to the PCB, but there’s no way to ensure you get a proper connection with the pads on the PCB. It will be a one shot deal - if you don’t get it right the first time, you’ll be out of luck on subsequent tries.

I need to be clear here... I understand that you need this laptop now so time is critical. This avenue of repair is highly likely to fail (though you could get lucky) and will end up costing you much, much more down time than if you took the time to get the right tool for the job.

How might it fail? You could mis-align the connectors or you could get glue/epoxy between the connector and pad insulating it. You’ll cause more damage trying to remove the connector to retry the repair

You might want to look up TV repair shops in your area as this repair would be something they could do as it’s a very simple job.