yes it is possible, and I am very interested in this topic also. Please read: http://hifiduino.wordpress.com/2011/09/30/arduino-leonardo/
, you can see that the new Arduino supports USB-HID class (HID=Human Interface Device), and in this class cathegory you will not need any driver on your computer, it will use the default one for MIDI.
The big step ahead of leonardo is that the USB interface-protocol is fully programmable, hence your Leonardo can act as USB mouse, keyboard, MIDI, as well as USB storage or USB-serial converter.
The big problems is that you need to have a USB protocolstack running on Leonardo, and for me it is not yet clear how to do it. I have had a look at the following stacks:
- AVR USB Stack
but I wanted something where the source code is simple and clear to understand (I want to learn some USB internals). I am looking into this direction...