Actually, no. UMA-equipped phones support what is called Unscheduled Automatic Power Save Delivery, an extension to wifi which reduces wifi battery consumption

Actually, no. UMA-equipped phones support what is called Unscheduled Automatic Power Save Delivery, an extension to wifi which reduces wifi battery consumption both when idling and when on a call to about the same level as a cell connection. UAPSD (branded as WMM Power Save) is part of the WMM WiFi extensions, which are a part of most consumer wifi routers.