Q: will it cause more damage if I continue to drive with a burnt out valve in the engine?

Hi there, thanks for writing in.

Unfortunately, yes you can do more damage by continuing to drive with damaged valves. The misfire will cause damage to the catalytic converter, which is a critical emission device. Damaging the catalyst can cause it to break apart internally, leading to plugging up the exhaust and causing an even more severe loss of power, which will make the car very difficult to drive. Eventually this plugged exhaust can damage the rest of the engine, eventually leading to a complete failure. This entire process may not take long at all, as catalysts are damaged very quickly from driving while misfiring. It will also be running much dirtier than usual, and is extremely bad for the environment.

I would strongly suggest having the problem fixed, or not driving the car until it is. If you decide to get this fixed, feel free to contact a certified mechanic, such as one from YourMechanic, who can diagnose your rough driving symptoms and help you fix it accordingly. Good luck.