Can't tell you the system specifics but have flown one with the capts rad alt failed (twice actually), and the EGPWS and GPWS were fine.
Our winter sim a while back was also based on this failure :
While gear is not down, effects are :
i) With either throttle at idle EICAS warning GEAR NOT DOWN, with no aural alert.
ii) With either throttle at idle and flap in any position other than up, EICAS warning GEAR NOT DOWN, with aural alert.
iii) With either throttle at any position and flap at either 25 or 30, EICAS warning GEAR NOT DOWN, with aural alert.