I would expect that on most devices with switching power supplies, like most players, there would be no effect. On units with conventional power supplies like amps, there may be some possibility of the noisy output of many less expensive UPSs could make its way through, but unlikely. With amps, the larger problem that I would expect is peak and sustained current availability.
I don't have time to search for it now, but Audioholics did a couple of articles along with a tour of APC's home theater product division.
I believe their conclusion was that standard computer UPS are not ultra stable and free of noise, since computer power supplies can handle this without much problem. Also, computer UPS cannot handle the instantaneous current draw that some larger main and subwoofer amps demand. This is why APC developed a line specifically for home theaters.
Personally, I think it is overkill. The only device I would want on one would be a projector so that it could go through it's cool-down period in a power outage. If you have an HTPC, that might be nice to have on a UPS to protect the hard drives and OS integrity.
Most "consumer" quality UPSs are not true on-line systems, they don't do ac-dc-ac conversions and the ones that do aren't built for ultra clean/stable output. I doubt there would be much impact on sound quality and I agree most can't take the bursty high amp loads of an audio amplifier. I would run a UPS on anything that would require a "soft" shutdown if the power fails, and an isolation transformer on everything else..