The GENESIS mission prepared for launch in 2027 integrates the four space-geodetic techniques on a single spaceborne platform in medium Earth orbit. With its unique observations and alternative tie concepts, the mission aims to contribute to an improved accuracy and homogeneity of future terrestrial reference system realizations. To assess the expected contribution of Global Navigation Satellite System (GNSS) tracking, a comprehensive GNSS coverage analysis is performed based on detailed link-budget simulations, taking into account the best available gain patterns and signal-specific transmit power estimates derived for this work from measurements of a high-gain dish antenna. The benefit of different receiver antenna concepts for the GENESIS spacecraft is assessed and it is demonstrated that a single-antenna system with either a nadir-looking or side-looking boresight is a viable alternative to the dual-antenna configuration considered in initial mission studies. Compared to terrestrial users and missions in low Earth orbit, GENESIS will collect GNSS signals transmitted at up to two times larger off-boresight angles. Only limited information on the actual transmit antenna phase patterns is presently available in this region, which hampers a quantitative assessment of the expected measurement and orbit determination accuracy. As such, a comprehensive release of manufacturer calibrations is encouraged for all blocks of GPS and Galileo satellites. In parallel, a need for in-flight characterization and calibration of the GNSS transmit antennas for off-boresight angles of up to 30 deg using observations of the GENESIS mission itself is expected. The impact of such calibrations on the overall quality of terrestrial reference frame parameters will need to be assessed in comprehensive simulations of global GNSS network solutions with joint processing of terrestrial and GENESIS GNSS observations