Do auctions time remaining still count down when the auction house is offline?
Yes, the AH auctions still count down when the AH is unavailable.
I noticed this behaviour on the Americas region's AH as I put some auctions up in between two longish AH outages last week. When the AH came back up, the auctions had counted down significantly even though there was probably only 15 minutes between me putting the auctions up and the AH going down.
Edit: Blizzard (relatively) confirmed the behaviour (Source) you see in game by not classing it as a bug:
I can't confirm 100% but I believe it does not pause.