There's a thread on the BioWare Social Network started by someone who had to create a new account to post there, because his original account is still enduring a 72-hour suspension for what was deemed an inappropriate forum post (he says he agrees he deserved the forum suspension for posting "Have you sold your souls to the EA devil?"). In a surprising turn, he says that besides keeping him from being able to post to the forums, the temporary ban is preventing him from activating his copy of Dragon Age II, which, as noted on Kotaku (thanks nin), is especially odd, since this is a single-player game. There was a similar story in 2008 that resulted in EA explicitly denying that forum offenders were being banned from games, but this thread concludes with a moderator explaining that under certain circumstances, an EA forum ban can indeed prevent access to your games:

Please review the EA Community Terms of Service, particularly sections #9 and #11. There are two levels of enforcement here:

1. BioWare community bans are forum-only and can be for as little as 24 hours. These bans should have no effect on your game, only your ability to use all the features of this website/community. these bans are handed out by BioWare Moderators as the result of our travels around the forum and/or issues reported by fellow community members.

2. EA Community bans come down from a different department and are the result of someone hitting the REPORT POST button. These bans can affect access to your game and/or DLC.

Because the BioWare community now operates under the same umbrella as all EA Communities, community members here have all explicitly agreed to abide by and be governed by both sets of rules. Consider it an added incentive to follow the rules you say you're going to follow.