MIDI Jack and MIDI through USB simultaneously


I am wondering, can someone use MIDI IN/OUT jacks, connected to pins 0 and 1 (RX and TX) to interact with MIDI hardware, at the same time that the arduino interacts via MIDI with an application?

I am using an Arduino UNO, and the HIDUINO Firmware for the AtMega8u2, and the midi library

I just don't seem to find a reason why that wouldn't work, other than that I've never seen it before, anywhere, and that I've always thought of the serial as a p2p protocol.

If I send a midi message through TX, it will go to the application as well as the midi hardware, and if I get messages from the application, the MIDI library should handle it as well as if I get messages through the MIDI IN jack...

What am I missing?

No one?