XPCOM likely includes such functionality as part of the testing rig. Mochitest at least is capable of this (again, probably though XPCOM).
On the other hand, when a user is on the system this a generally a gross violation of user interaction practices. Be sure you have a good justification for doing it. It may seem convenient but what if they're doing something else whilst using your addon? I usually have various apps open at once, Fx extensions are only part of that. I don't want it taking control of my mouse, EVER.
Is there something wrong with setting the focus? At least that only forces the user's hand at a window level.
It also suspect it make it quite difficult to get past AMO review. You'd have to justify why it was necessary to invoke such low-level functionality. If you interact with a window, for example, the window might be able to affect the input of your functions which in turn control the mouse... and then a random web site has access to the user's window!