Absolutely. This works great in my G3X aircraft.
Page F-4 of Rev. E of the G3X installation manual defines the wiring from the GSU-73 to the GTX-327 transponder.
It also includes the following configuration information for the GTX-327 (which you have probably already done):
GSU 73 TO GTX 327
A. ON THE GTX 327 CONFIG MODE PAGE, SET THE CONNECTED GTX 327 RS-232 INPUT FORMAT TO "REMOTE"
On the GTX-327, also make sure it is configured for "Automated Airborne Determination". If you have any trouble figuring out how to do this, come back and ask here and I will dig up the instructions.
From GTX-327 Manual:
Automatic ALT/STBY Mode Switching
If the GTX 327 is configured with Automated Airborne Determination, ALT mode selection occurs when lift-off is sensed. When the aircraft is on the ground, the transponder automatically selects and displays STBY