There are a couple of caveats there, though: not all UPSs are equal. Some of them do do a very good job of power conditioning, and filtering out RF and narrow transient spikes. Some of the cheaper ones, however, do not do this very well, if at all: so depending upon a UPS to handle all of your powerline noise issues may not always work.
It gets worse. Some of the _really_ cheap UPSs put out essentially 60Hz square waves at 120V out of their inverters- they don't lowpass filter after the the chopper at all. There is a lot of equipment out there that doesn't tolerate that very well: most power supplies really like to see a sinusoidal input, and the closer you are to that, the happier the gear will be. Some of the cheaper ones take a long time to pick up after a failure, too- 15 or 20 cycles. It's like anything else: the real bargain-basement UPS units are not likely to help as much as their marketing hype claims.
If you're going to spend the money for a UPS, spend a little more and get a really good unit. Here's a place where specs do matter. Good ones will do the following things for you: filter both normal and common-mode line noise from 100kHz up, put out a true sinusoidal waveform, buck overvoltage down to the spec, boost undervoltage up to the spec in case of a brownout, have a selftest that will exercise the battery periodically (it's not good to find out that the battery's gone only when the power fails, eh?), and pick up in the minimum possible time (2-4ms is good: 30-60ms will let some equipment such as PCs fail, if they have heavily loaded power supplies).
I personally use APC UPSs, and have for years- I have 9 of 'em supporting power to all my machines and my phone system, here in powerfailure country. They get used for real 2 or 3 times a month. There are other vendors of good ones as well. The good ones have a few things in common: they are large, heavy, noisy when operating, and worth every dime...
The cheap little desktop ones you can get at Comp USA that are about the size of a power strip don't even come close... If you can pick it up in one hand, it probably puts out square waves, doesn't do any input noise filtering, and won't work as well as you'd like. Caveat Emptor!