The video card would just output whatever is in the framebuffer at the given time. Provided that the video player outputs at 60 Hz with VSYNC, the monitor would always refresh 2 identical frames in sequence.
The question is whether the video player is capable of performing any temporal upsampling of video during playback.
I doubt that many video players implement this as it is a computationally very demanding task (requiring use of e.g. CUDA for motion interpolation).
Using a Google search I found a couple of video players that will perform motion upsampling from e.g. 24 FPS to 60 FPS - but I have yet to find software that upconverts to 120 FPS.
Today I tried to measure frame rate in player.
FRAPS shows 30fps for 30fps video, 60fps for 60fps video and so on. At the same time, for each case monitor shows 120Hz.
So, I think the board performs some FRUC. It looks like frame doubling.
But, I need more objective opinion than my eyes :-)