An OS upgrade or update on the Mac side of the partition wouldn't have any affect on the Windows side. The two OSs don't share any drivers or other software in common, and the Windows side can't even read the Mac side without special tools (or a much older version of Bootcamp).
Driver updates can make a difference on the Windows side though, not only an update of the driver for the mouse but also potentially a graphics driver or even something else entirely. Mouse lag or unresponsiveness can be caused by a delay in rendering the mouse, which would be graphics driver-related, rather than an issue between the mouse and the OS.
