Looks like at this point, joystick emulation is still a little bit of work as opposed to keyboard and mouse which just works.
The Leonardo would have to be programmed to make it all work. Here are two posts I found from people who have done it with information on how to replicate.
http://www.imaginaryindustries.com/blog/?p=80
http://blog.qwertymodo.com/2012/07/a...ad-part-1.html
With this, you should be able to plug in the Leonard and Windows will detect it as a joystick. Labview would never know the difference between it and a standard joystick.