First, you should figure out what your actual power consumption is. A 600W PSU only draws 600W if the hardware needs it. You can get a Kill-A-Watt or similar monitor in the $15 USD range. You can also get a decent ballpark number from online calculators 1, 2, 3. Don't forget to include your monitor.
The UPS you linked only supplies 300W. It gives 10 minutes as the backup time, and I'm going to have to assume that's at full (300W) power draw, as I don't see any other stats on the battery. So, no, it probably won't fit your needs.
You could take a look at the APC or CyberPower UPS selectors to get an idea of what would fit your needs and the price range.