Oh, absolutely not.
They only wanted the accounts linked so when I got into another support chat they could verify the purchase with screen shots of my steam purchase history and give me the game on Origin. The tech also didn't know that the steam login and screen name can and should be different, so spent most of the time explaining that. At least the DLC still comes with keys you can claim on Origin as well.
TLDR: Steam version online features are still not working, but I now have it on Origin as well after a couple hours of tech support.
