The AIM is an excellent reference for navigation. It's states authorization to use GPS for any IFR operation is based on several factors like;
-- GPS navigation equipment must be approved in accordance with TSO-C129, or equivalent, and the installation must be done in accordance with Advisory Circular AC 20-138D or equivalent. (there's nothing in that AC that suggest an owner can prove his non-approved gear meets TSO then be good to go)
-- Aircraft using GPS for navigation under IFR may require an approved and operational alternate means of navigation appropriate to the flight.
-- The GPS operation must be conducted in accordance with the FAA-approved aircraft flight manual (AFM) or flight manual supplement.
Flying with non approved gear is not going to end well if there is loss of separation.