No, you can't normally do that -- unless you played the game in a "Window" and not full screen. Few games allow that. Solitaire allows it

As do MAME and other games... but you get my point.
Your line of question basically is answered by: IT DEPENDS on the game.
I've seen some games that let you actually use BOTH screens. One for commands / status, the other for main arena. Etc. Matrox has a special part of their web site just to feature games that support this... and I think they pay developers to enhance the games...
Most games just give you a blank 2nd monitor...
Stephen