What would happen if I exceeded mach 1 over a regulated area?
It would be a violation of 14 CFR 91.817


  § 91.817 Civil aircraft sonic boom. (a) No person may operate a civil
  aircraft in the United States at a true flight Mach number greater
  than 1 except in compliance with conditions and limitations in an
  authorization to exceed Mach 1 issued to the operator under appendix B
  of this part.


It would be extremely easy to track such an aircraft, and the pilot would be dealt with upon landing.