What happens if 600W UPS is forced to deliver 800 watts by the PSU?

Solution

The UPS will detect an overload condition and shut itself down. That's assuming that the specific UPS has the proper protection circuits built-in.
Well, I need to disagree. I am using a 600VA/360W Zebronics UPS from 2 years with my PSU being 600W. Had no problems with the UPS, but backup time is like for only 40-50 secs, I'd just off my system instantly if my power goes off. I also dont have any performance issues too..