you cannot complete a published RNAV, GPS, GNSS, WAAS, EGNOS approach using such basic GPS equipment. You also as an operator require approval from the FAA or CAA together with the correct equipment before conducting these approaches.
What you can do legally is fly a non precision approach as a GPS overlay, providing you have monitored ground based information i.e. an NDB or VOR needle displayed.
Oh dear. Shall I start by asking for references? G-reg, private ops, or if you like FAR Part 91.