Inspired from this answer, you can make a fully transparent window that passes events through to the windows behind them.
However, it's also important to touch on a method I thought would work, but doesn't appear to work on my system, being a 64-bit Windows 10 Pro. This is largely operating system dependent, but I would like to think that, for security reasons, setting the global cursor is blocked on most, if not all, secure operating systems.
For a direct (as best as I can) answer to the question asked, no, you can not set the global cursor using Java.
