A new Electronic Arts Account Suspension Policy indicates that being forum-banned from EA's Origin service will no longer result in being prevented from playing single-player games (thanks Blend Games). Here's word:

If you find yourself with a disabled account, please note that you can still play EA games in single-player mode. For PC games you will need to enable Origin's offline mode to play games with a disabled account. Go to the settings tab in Origin (the gear icon) and select Go Offline.

If your account has been disabled, please follow the instructions in this article if you wish to appeal the action.