Dragon age Origins is one of the best games ever created imho. Id recommend playing that through at the very least, and maybe just read up a summary on DA2.
I think you'll be fine either way, altho. I just hope that they don't go too far. It honestly bothers me A LOT when the game makes you feel like it's treating you like an idiot because it has to explain everything that you already know. And then you get characters that are meant for the newcomers that barely have anything to them whatsoever since they don't have any time to grow. I mean, you don't watch lord of the rings 3 and just expect to know EVERYTHING. Sure, you'll catch up on the plot, but there will still be a lot of holes in it if you haven't watched the previous ones.
ME3 felt like it went WAY too far in that direction. I didn't feel like I was playing my Shepard at all, and the new characters felt so out of place. I yelled at the screen at times because Shepard said such stupid things at times.
I understand that they want to branch out and sell as much as possible, but it just really bothers me when it detracts from the game for everyone who have followed the series from the beginning. If you walk into the third part of a trilogy, then you only have yourself to blame when you don't get what's going on tbh.
But I think that you'll be fine in this case, since the protagonist changes.
DA:O - Awakening expansion + DLC's = Grey Warden
DA2 + DLC's = Hawke
DA:inqusition = Inquisitor.
So, it wont be that bad I suppose. You might just miss out on some cameos. If you end up meeting Leliana for instance, but even so. The inquisitor wouldn't know who Leliana was either way, so it doesn't matter all that much I suppose.