Yes, Sean, you can do that. Simply cut off the USB plug that is currently plugged into your Rosetta and then splice the Pin 5 wire from the FX onto the orange wire that is currently connected to your TT21 Dsub and do the same with one of the FX grounds.
This is exactly what I did when I pushed traffic from my FX to the Dynon HDX. It previously had the FTDI USB to serial converted plugged into the Rosetta and then into the HDX Dsub. Instead of taking the Dsub apart and employ my awful soldering skills, I just spliced FX RS232 Tx to the orange wire that was on the FTDI USB.
Your TT21 is probably already set up for GPS in via the NMEA 0183, so just make sure the two baud rates are the same and you'll have ADSB Out from your TT21.