So I dropped it off at the shop and headed into work. About an hour later they called me back. The wires leading to the spark plugs had gone bad and were leaking voltage, causing the plugs to misfire. So they definitely had to be replaced because if I didn't, I would end up ruining the catalytic converter and then a $300 repair would turn into a $2,500 repair.
I shouldn't be entirely surprised that this would happen, the car is about 11 years old now. So the car is fixed up and driving again, thank goodness.