I redeemed the DLC key through the Origin client, which is what prompted me to ask the question in the first place. If I try to redeem on the Bioware site, it tells me the key is already redeemed.
I'm not really sure on the redeeming on Origin part. When I did it it was before the Bioware/Origin account mergers so they weren't cross populating or really talking to each other and I actually had to redeem through Bioware.
now you can do it on either or and it will populate over but not 100% sure on that point.
I also noticed that the Bioware social account will let you redeem DLC for games you don't own. For example I grabbed a key from Alienware for an M-90 Indra sniper rifle for ME3
and it let me redeem it to Origin and shows up on my Bioware social account although I do not own ME3.
Actually based on that recent experience I'm going to go ahead and say that redeeming Bioware DLC on Origin now does seem to populate it over to the Bioware site.