There are apparently some PSU's that will not work with lower powered UPS's but I don't know any specific cases, and if it's running off utility power it shouldn't matter. In any case, I don't really see the point in running a 600w PSU through a 300w UPS as it's not going to work if the power switches which is the whole point of a UPS.
If you're buying a UPS you also need to look at the VA and think about the other stuff you runoff it. For your rig, for it to work properly, you would want 600W/1000VA as a minimum I would think, maybe more depending on your monitor.