The "sort of" part ... The motherboard LED is powered by the small, always on 5 volt standby power supply. It provides initial startup voltages to the rest of the PSU.
The "not exactly" part ... It has nothing to do with the main section of the PSU that provides operating power to the computer.
Well, I was actually referring to the condition of the PSU, whether or not it's totally dead. A partially functioning PSU didn't really came across my mind, since I don't know if a PSU can be partially functioning only on standby 5V yet can't supply any power through the connectors. AFAIK, the 5V supply also came from the main 20/24 pin connector. But maybe you know about this better than I am.