if you do a game, probably you need a fast rendering, so you need to use something with OpenGL ES, cocos2d is a nice framework on top of OpenGL ES, so yes...cocos2d can be very usefull for games.
To manage multiplayer in this particular case i would prefer to have a server to manage things avoiding to implement a server\client solution directly on the app.
You can take a look this tutorial, it should be a good start.
How To Make a Multiplayer iPhone Game Hosted on your Own Server Part 1 | Ray Wenderlich