Will Photoshop CS version 8.0 work if I update from Tiger to Leopard?
Yes, 8.0 runs even in Snow Leopard.

Also:  look in the Help menu and see if there is a "Deactivate" choice.  (I think 8.0 is before that started, actually.)  If so, then you should deactivate Photoshop, install the new OS, then activate it again.