Does wifi on iPhone use up my *home* data plan?

This may be a stupid question I can already guess the answer to, but I Googled and can't seem to find a response for it:

I'd like to know if wifi on the iPhone is sucking up bandwidth (that I am being charged for if I go over the cap) from my ISP on my home internet connection? (I'm not conncered about any phone data plan, as I don't have one).

I just discovered radio stations on the iPhone, and I'm wondering how much bandwidth on my home internet connection it will cost me if I listen to wifi-streamed radio all night, on my iPhone? Or a couple of hours a day of watching streamed tv on the Iphone?