No. Each Dragon Age game pretty much ignores Origins. Dragon Age II... might help you understand Inquisition, a bit. But they also skip time between DA2 and Inquisition, so even then, you've got to put the pieces together yourself.
To be fair, there isn't much in DA2 that has a direct impact on DA:I (other than knowing Varric a LOT better - and seeing the much better written and portrayed version of his character in DA2 - which will make you appreciate him more in DA:I).
The key thing you kind of need to connect DA2 and DA:I is the Legacy DLC. It's the only thing that really touches on the DA:I narrative at all. Almost everything else from DA2 gets summed up as much as it needs to when you ask Varric about his past, people he knows, and what they're up to now.
DA:O has SOME effect on DA:I (especially if you did the Dark Ritual and/or romanced Morrigan or Leliana, and how you handled the Alistair/Loghain issues), but ultimately, someone could easily play DA:I first without knowing a single thing about the previous games and still get about as much out of it as everyone else does.
Unfortunately, you won't get much out of it regardless because it's basically half of a worthwhile Dragon Age plot padded out with nonsense, plodding, and grindy busywork... but it doesn't really REQUIRE you to play the previous games to "appreciate" it.
Well the reason I figured DA2 helped with Inquisition is because of the whole mages/templars thing. ---