Nothing happens to the visual output on the monitor, the monitor will simply refresh the same frame.
If your framerate is dropping however, this means games may appear to be less "smooth" visually, due to less images appearing each second.
Will the card/monitor cut the frames in half to allow for double refresh inbhwtween frames, thereby making my games play at either 30 or 60 fps? Or will they play fine at in between number such as 47 or 51 frames?
Will the card/monitor cut the frames in half to allow for double refresh inbhwtween frames, thereby making my games play at either 30 or 60 fps? Or will they play fine at in between number such as 47 or 51 frames?
No, it should run at whatever fps its at.
But like I said, the game may visually stutter at lower than 60fps.