No, wifi does NOT use your plan data allowance. The CSR's you talked with are completely WRONG on that point.

However, having said that, some Apple iPhone users have claimed otherwise and I don't dispute them, because it IS technologically possible to BOND wifi and mobile data streams (either by intentional or faulty hardware and software design) and there ARE industry initiatives to do this over carrier-owned wifi access points in the near future.

Depending on what phone you have, to be safe, if you can turn OFF Mobile Data on your  phone when using WiFi, do it. I can on mine, and i've never  seen data usage I didn't expect, and I use WiFi frequently as i'm only on a 2 Gig plan.