As gene said, if you choose a reputable one, it should not be an issue. The real issue is, this monster amp apparently has a 4 kVA transformer and can output a maximum of 300WX5 into 8 ohms or 600X5 into 4 ohms. Assuming the amp is 50% efficient, to output 1500W it has to take in 3000W, or close to 4000VA. So your 2200 VA, or 1600W UPS is not going to cut it. It will work (very rarely would an amp be required to deliver their maximum rated output to all 5 channels), but you may not benefit from the amp's full potential, depending on the kind of music/movies you play with it. This is only from the VA/W stand point. If that UPS has some sort of filtering device and/or current limiting device in series, it may or may not have adverse effects on your amp.
By the way, does the amp allow you to use two 20A circuits? If not, I hope they come with a 30A power cord so that you can run a separate 30A circuit for it.