Ultimately, the answer is "No. You cannot bind to the controller if the GPS unit is not plugged in".
But..... The exact wording of your question brings doubt to the understanding of your meaning. You asked specifically if it would bind. In reality, it won't even come close if the entire GPS module is unplugged (which is the first guess at your meaning) . The first (and only) thing you would see would be a failure of the board to even initialize. You would never reach a stage where binding would be a question or a possibility. That means more information is needed to provide a real answer.
1.) Are you getting beep tones and flashing red rear main LED when you power on the drone?
2.) Do you have the actual GPS connection plugged in, but perhaps one or two pins are not seated?
3.) Do you have the GPS completely unplugged? If so, what is the reason and is the GPS available to plug it back in?
4.) Did anything happen between the last time the system worked correctly and the first time it did not? Things like long storage periods, hard landing/crashes, significant location changes, modifications/repairs, equipment changes, firmware updates or anything else you can think of.