Yes, the mouse has to have the ability to sense what it's connected to and shift electronic gears internally. Generally, if the mouse doesn't ship labeled as a "universal mouse" and come with a PS/2 adapter, then it won't work as PS/2 with a "generic" passive adapter. Keyboards are the same way - if not marked as "Universal' nor comes with an adapter of its own, then it is USB only.
Unfortunately, Logitech has fewer "universal" products than in the past so you have to be sure you know what you're getting if you need/want PS/2 compatibility.
.bh.