If a button is configured on Mac, does it still work after switching to Windows?

If a button is configured on Mac, does it still work after switching to Windows?

Yes. As long as you assign commands from the Glide list, both the Mac and Windows mappings are written back to the mouse together. When you switch systems, the firmware automatically sends the command for the current OS, so it won't stop working — even if you've never set it up via the software, the firmware sends the OS-appropriate command.
The only exception is a custom shortcut (a key combination you define yourself), which is a fixed value and may not carry over across systems.