It depends on how much you're drawing really. If it's a whole bunch of wall-warts that aren't drawing much but won't all fit together on the half dozen powered outlets on the UPS, then I don't think it would be a problem. I've got just a dollar store power strip plugged into one of my battery powered outlets that powers my speakers, a 13.8V/5amp power supply for running my CB radio, a lamp with LED bulbs in it so that if the power goes out we have a normal light to turn on in the house, the printer and the cordless phone base. My PC and monitor however are plugged directly into the UPS.
I just run everything I can that I remotely value off the batteries so that not only are those items protected from surges, failures, etc., but they also get much cleaner, regulated input power and less of the "noise" from the mains.