I have an APC Back-UPS ES 400, and during a brief power failure (less than a minute), its buzzer sounded continuously. Looking up the manual, this apparently indicates an overload. It's rated to 240W, and it's definitely plausible that the computer connected to it could exceed that since it was running a game (maybe 10 to 20W over by my estimate; I can't measure it).
The buzzer stopped when power was resumed, and the PC still works fine, but I'm slightly paranoid now that this could have damaged the PSU or other components.