Currently grunking away, but I'm certain that if Jack really was trying to get off with a teacher, he would want little to no identifying information about himself being drip fed to her 500k followers.
Mr Coffee and several friends of mine are teachers, and in this age of social media it is almost a military operation to keep yourself out of the public eye so that nothing you say or do can come back on you. If the teacher is real, Jack will NOT be able to keep her mouth shut about him enough for him to remain entirely anonymous. We already know he teaches English and he's local enough for a date, a few more bits like that and I'm sure he can be traced.