I do have a UPS. Compared to the Windows machine I have my Mac Mini takes no time at all to boot. It never ceases to amaze me!
It does boot pretty fast, even without the tricks Vista plays with flash memory. I've used and played with Macs a lot before, but this iMac is the best of them all, definitely better than any Windows box (and even better at being a Windows box than my other Windows boxes).
Is your UPS plugged into the Mac via USB?
Instead of all this guessing I just decided to do a test. I set my power settings to turn off the computer if it goes on UPS power. Then I put it to sleep and unplugged the UPS. It woke back up and shut itself down.
You should get approximate results with the mini if you have it connected to the UPS with USB.