I am not a doctor, nor am I you. So keep that in mind with anything I say.
In a low bar back squat, the cervical vertebrae are not underneath the load of the barbell. For most people, the bar probably passes over T2 or T3. However, the neck is certainly involved in squatting. I would suggest keeping a neutral cervical spine by looking down while squatting. You will be able to tell me how all of this feels better than I can predict for you. In general, however, people don't herniate cervical discs from squatting, although I could see looking up being problematic. I would also be sure that you do not drive your head into the bench on bench presses.
My advice? Be careful, but try it. I bet you will be okay.