Will a faulty throttle position sensor cause rough idle?

In all probability not. If you have a check engine light on then you will need to have it scanned for codes. If the code shows a component, such as the TPS, it DOES NOT mean that is defective. It only means the problem lies in that area. That is what you pay a technician to let you know. It is cheaper to know what is the problem, than to throw parts at the car.