Set the unraid to not automatic start. That way you can confirm everything is ok before you start all the services. It's a very bad idea to run the UPS to empty and immediately start everything back up when power returns. Many times the power will go back out again for a little bit after the first time it comes up, and if the UPS batteries are already drained, there will be no way for it to successfully shut down again, plus it's very hard on the UPS batteries to fully drain them.
There are only 2 likely scenarios I can think of, either the power goes out so rarely that waiting for your servers to come back on line isn't going to happen hardly ever, or the power goes out so frequently that you really need to rethink the use of just a battery backup, possibly an inverter with a bank of batteries to allow you to ride them out.
Either way, automatic restart after a power outage is a bad idea, you need to evaluate each individual situation before you get everything running again.