Normally when you are just sitting at the windows desktop and doing basic things your GPU downclocks to "2D mode", this gives it enough power to do basic things and significantly reduces its power consumption, when you need it to do some heavy lifting it kicks up to 3D mode clocks. For DVI/HDMI signals there is an end of frame blanking signal after each frame, this is relatively long and on single screen setups this gives the GPU a time when it can change its memory clock and not impact the screen as the screen isn't expecting a signal. For multi-screen setups you cannot ensure that all screens have their blanking signals at the same time and if you try to change the memory clock while it is feeding data to the monitor you will lose that frame and get a black screen for a frame or two, thus the easiest way around this problem is to simply never change the memory clock and leave it at full speed all the time.
This isn't an issue you have to deal with, the drivers already know what to do. One thing to be aware of with two screens, some games are dumb and suck at locking your pointer to the screen in use, Empire total war on a battle if i move my mouse too far to the left it pops out of the game window and onto my second screen, it is not confined to the active window. Most games are fine with keeping your pointer inside though, just don't be too surprised if you stumble across your pointer popping out.
Overall though, i must say 2 screens are vastly superior to 1 and you won't be disappointed.