Will find my iPhone work if cell service is disabled

Hi-

Lost my iPhone 4S when it was in wifi-only mode. Verizon suggested I disable service just in case, which I did. But does that mean the find my iPhone app (which I already had configured/enabled) won't be able to find my phone? Or can it still identify the device if it connects to wifi?

App correctly identifies the phone as being offline, meaning whoever found it hasn't activated cell service and/or can't even access phone b/c it might have been locked (unsure).

Thanks.

-jb