This should work. The GarGraves site shows an 18VAC power supply, but I suspect anything in the 14-18V range would work. The Lionel UCS track allows for external power, and that's essentially what this is doing, only with the GarGraves.
Both have Left Control Rail (LCR), Right Control Rail/Coil (RCRCL), and Ground (CL) connections. On the GarGraves track (CL) connects to external power through the control box. The fourth connection on the Lionel UCS track, which isn't needed for this configuration, is for power from the center rail to the control button box.
If it's wired correctly, looking at the 4-conductor ribbon cable from the UCS control box:
The left conductor is ground. This connects to the return side of the AC power supply and the track 'CL' connector.
The 2nd conductor from the left connects to the track Left Control Rails (LCR).
The 3rd conductor connects to the 'hot' side of the AC power supply.
The 4th conductor, on the far right, connects to the Right Control Rails and the other side of the coil (RCRCL).
And that should get you up and running.