UPS vs PSU wattage during normal operation?

Does a UPS battery backup act as a funnel for wattage during normal power operation (e.g. full power is coming from the wall outlet to the UPS)? I ask because I have an older UPS with only 330W output during a power loss event, and I have a PC with a 750W PSU and a relatively high-power graphics card. If I plug the PC in to the UPS, could damage occur due to not enough power coming from the wall outlet - UPS - PSU, even when NOT on battery power?

Question by Mike Lasch on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.