You'd need to check NOTAMs confirming that the runway closure has no impact on the IAP in question, eg raised minima or even NTBU.
Assuming not, then as it has a circling minima and is the only IAP for the AD, you'd be reasonable to assume the approach is available (perhaps on request). The question should be directly asked preflight by telephone to the responsible ATC/FIA manager for confirmation.
I've used IAP to closed runways for circling to intersecting runways without guilt before.