How to detect/monitor AC power
If you pass a few mA through the contact, and it is a signal type with sealed contacts it should be reliable. I'm not a big fan of reed relays. 

You could also use an optoisolator rather than a relay. You'd need a couple resistors (for the input and a pullup on the output). 

There are also modules made to accept an AC input and provide a logic level output, probably $15 or so. That would get rid of the adapter and the relay (Photo from Digikey).