It might seem like multiplayer games use a lot of data, but they actually use a tiny amount of data. All that gets sent to and from the server are tiny packets of data that communicate player locations. You would have a very hard time breaking any data limits if you are only playing multiplayer games.
One thing to be careful of are game updates. Patches and other things that need to be downloaded to make a game work can often be quite large and if anything is going to break your data limit it will be this.