To use the equipment suffix "G", does the GPS have to be certified for IFR flight?
Yes, using GPS for IFR requires a certified unit. The AIM 1-1-17(b)(2) says (emphasis mine):
Authorization to conduct any GPS operation under IFR requires:
(1) GPS navigation equipment used for IFR operations must be approved in accordance with the requirements specified in Technical Standard Order (TSO) TSO-C129(), TSO-C196(), TSO-C145(), or TSO-C146(), and the installation must be done in accordance with Advisory Circular AC 20-138, Airworthiness Approval of Positioning and Navigation Systems. Equipment approved in accordance with TSO-C115a does not meet the requirements of TSO-C129. Visual flight rules (VFR) and hand-held GPS systems are not authorized for IFR navigation, instrument approaches, or as a principal instrument flight reference.