Can you output to D+ and D- so that Arduino Uno can be used as a USB device?
Not with an Uno, no. You can only use USB Serial (CDC/ACM) through the on-board USB chip[1].

Your best bet is probably with a Teensy 3 (or 3.1 or whatever they are up to now) which has built-in support for USB MIDI emulation.



1: I believe there is MIDI firmware for the USB chip on the Uno, but installing that requires a hardware programmer and then breaks the normal sketch upload.