Well a router is just to add more access to a modem, which is what gets you the access to the internet and is needed to even have WiFi (someone has to have the modem). Or they can be combo devices. Both modem and router.
As long as the phone you are wanting to access works, will turn on and has WiFi capabilities, then yes you should be able to use it for WiFi. Just remember to turn off "Data" in your phone's settings so it won't try accessing that instead. Also, remember that you won't be able to use the text messaging or phone call making part of the phone with only WiFi. You would need apps for doing that.