According the A320 QRH you need a standby attitude indicator for CAT II and CAT III approaches.
So if it fails, you are limited to CAT I.
But no indication of landing capability will be given in the Status.
Normally you have to go-around below 1000ft.
(Unless you are below the alert height during a No DH CAT IIIB approach)
Edit: a320_richie was faster!
