Don't actually unplug it, switch off the power to the outlet. Removing the plug breaks the ground circuit, and has the possibility of damaging equipment as any current imbalance travels through network or other still connected cables.
You can do a full live test without hurting anything, but it's a little complicated. You need 2 power strips, plug the UPS into one, and the stuff that's normally plugged into the UPS into the other. Approximate the load as accurately as possible, and load up the UPS output to match. Incandescent light bulbs make good small loads, space heaters for stuff above 250ish watts.
Run the server up to typical usage, all containers and VM's running as normal, then turn off the power strip running the UPS. The UPS should signal the outage, and hopefully the server will fully shut down before the UPS quits powering the dummy load. Ideally it should be totally done before the batteries reach 50% charge, so as not to stress them.