The rusted resonator will not cause a driving problem for you, you may hear more noise since there is probably a hole in the exhaust. This doesn't mean that it shouldn't be fixed however. When there is a leak in the exhaust system there is always a chance that it could leak into the passenger compartment, you don't want to breath that! So while it shouldn't be a problem for you to drive the car, it should be repaired.
Ladies Start Your Engines
Having a rusted out resignator will not cause your car to break down, if that is what you are worried about. It will just be very loud. The exhaust resonators job is designed to lessen the sound of the combustion. The down side to having a rusted one is, the rusted resonator is releasing the toxic harmful emissions gasses into the ozone layer.
〉 Answered on Nov 24th, 2010 by Audra Fordin, Owner at Great Bear Auto Shop
I would look into having an estimate on replacement but you Can run with it rusted.