The demo of FH4 is just the same as the start of the FH4 game so there would be no point in playing the demo if you have the full game. I've never heard of someone playing the full game and then going off to play the demo but I imagine the save should be okay probably.
But, again, the FH4 demo is just the beginning of the full game...I know this as I played the demo version before purchasing the full game. There's nothing different between the 2 so playing the demo is pointless