Yes, it has laser ring gyros as well as accelerometers, but so does the ISFD. The SAARU can only do three minutes of backup nav to keep the more advanced autopilot modes (APP, LOC, FPA, TRK SEL/HOLD...) available to allow for a graceful failure by supplying track, GS, cross and along track acceleration to the AFDS. Afterwards it does attitude and air data only - FMC position will be from the GPS only.
If the ADIRU data goes invalid, the SAARU does not follow the ADIRU outputs. The SAARU continues to calculate backup navigation data independent of the ADIRU. The ring laser gyros do not supply sufficiently accurate data for autopilot operation for extended periods of time, therefore, the backup navigation function goes invalid after 3 minutes.
Ref AMM SDS 34-20-00