Nope. That's been threaded about, again and again. The Apex can get power from either the EB8 over the AquaBus or the 12v. And it doesn't care if you have the 12v or not so you can't plug that into the wall and think it will alert the base unit. 12v is optional on the Apex. If the EB8 is on a UPS, then the Apex never sees the power go out.
If you really want a couple of critical devices to run, then put them and the 12v on the UPS, plug the EB8 into the wall. You won't be able to control those devices but if they're pumps or powerheads, then they're probably on all the time anyway. That or get a second EB8.