The general answer to the question is yes, you can activate it on origin. There are a few exceptions, like games that just aren't available on origin, but when I was in the chat with a representative getting my DAOUE activated (the code from impulse was only wanting to work on a german version, so I got them to activate the english version) she told me that just about every EA game from the end of 2009 and newer will activate on origin.
Basically, if it doesn't activate, click the help button in the top right corner of origin, and they should get it added for you.