Dual Screen Setup?

Yes, that would work, however, some games (as you said you wanted to play on it) either capture the mouse in the dedicated screen and you won't be able to move it to the other during the game OR they do not capture it and it will make scrolling in RTS or similar games, where it is done by moving the cursor to the edges of the screen almost impossible.
The first option will not allow you to "do other stuff" while the second does.
Some games can even be set to use both screens, either to broaden your PoV (with the result of the crosshair in FPS being in the middle of both screens making it rather akward to use (NB: using a thrid screen in the setup can help!)) or to use one screen as the main game screen and the other to place any GUI, info, radar, map etc.

Would I recommend to game on one screen and "do other stuff" on the other?
Probabaly not.
If other stuff happens to be even only slightly related to work, you are going to ignore it anyway .
If you're surfing the web while playing, that may greatly reduce your gaming experince and immersion (good for long loading times, though!).
What is a useful activity is watching a match on one screen and playing a casual game on the other during commercials or boring phases so you can use your spare time most efficiently
Other than that, you'll really have to see for yourself.

Thenically, apart from the stated ones, there aren't any limitations I have discovered.

Coming up next - useful links:
• If you like this project, please support it with your donation!      • Grab your HW info (HWIDs) here!     
• If you are a newbie, be sure to check out the DriverPacks tutorial!     • Here's how to create your own DP!