If the PSU is 80% efficient, and it is 600W rated, that means that under 100% load it will draw 750W from the UPS. But your computer components need to draw 600W to get full load. If it draws 400W from the PSU, the PSU will draw 500W from the UPS.
UPS power output of 650 VA is equal to 650 W if the power factor of the PSU is 1 (which is never). If you have a PSU with active PFC, the power factor should be close to 0.9, or to be safe let's say 0.8, which would mean 585 W or 520 W max power output of the UPS.
But if the PSU does not have active power factor correction, and the PF is 0,5 it means that the max output power of the UPS is half of the VA rating, 325 W.
If the max power draw of the UPS is exceded, the UPS should have protection, and nothing will happen to it, but the compter will freeze and/or shut down.