You could, but I wouldn't recommend it (you would need additional hardware to connect it to the Arduino, and you would still be unable to use the serial monitor for debugging).
If it's just for quick testing, use Hairless, if it's for a permanent project (and if you need your PC to see the Arduino as a MIDI device), get an Arduino board that supports MIDI over USB natively.
Does the MIDI keyboard you intend to use have 5-pin DIN connectors? In that case you don't need a MIDI USB interface. If your MIDI keyboard has a USB connector for MIDI, it's probably a device port, and a MIDI USB interface won't work either.