Great question — answering as the UphillTech team:
No you should not have to replace the drywall if the paper is not burned. Drywall is a fire barrier and can withstand high heat for short periods without losing strength or integraty. I would clean it well first repair the patch and use a good primer like Kilz and repaint.
Full answer by Merrill M. Meyers Jr.: https://diy.stackexchange.com/a/109473 (CC BY-SA 3.0).
Need it done for your business? UphillTech.
