A clock that could work is one that has the atomic feature that receives radio signals as soon as it turns on. The only problem to that would be is that the frequencies for atomic radio signals isn't in the receiving range of the PSR-500.
I have a PSR-800 with a clock, but I can only read it when the scanner is plugged into power, and the scanner is off. It's only function is to provide a time/date stamp for the .AU files when recording. Otherwise, useless.
Why not have a clock that's set by an on-board GPS system that can also be used to (optionally) select the nearby systems and the closest tower on a multi-site system. That would be something worth having.