I'd say up to a certain point. It depends on how much currently have.

You should be able to at least start the game with 4GB+. What will happen is if you run out of ram the game will start slowing down and stuttering, or it could even crash. The reason they call for 6GB minimal is because when playing TW3 you are going to be using up to 6GB total ram (OS etc.. included) while on lower settings. I wouldn't buy the game unless you are prepared to buy whatever parts you need to meet minimal spec.

If ram is the only thing you are concerned about, just pick up some more. 8GB is enough to get you by for quite some time and DDR3 is fairly cheep right now.