Actually, interesting question. I would think GLS approaches are unavailable, but neither the FCOM nor the QRH (FMC fail checklist) says so. There is an additional GLS fail checklist, but that only states that all ILS and non-ILS approaches are still available, which includes IAN stuff, it is used when the additional GLS fault light on the IRS panel (aft overhead) illuminates.
After all GLS is not LNAV/VNAV or IAN, it compares your (ground augmented) position in space against the ground transmitted approach geometry, no clue if that is done in the FMC or in the MMR but i would suspect it's the FMC.