RAIM is essentially peculiar to stand-alone GPS receivers, and may or may not include a FDE (fault detection & exclusion) facility. In an integrated avionics suite with certificated GPS the RAIM function is most likely to be performed by an "equivalent " software process. This will involve input from other navigation sensors.
Whether or not this allows for procedures to be flown during predicted RAIM outages I cannot say. That would be covered by national rules, and/or op specs I would imagine.