Quoted directly from Stephen Reid on the community forums.
No, you won’t.
While Origin will be the exclusive digital retailer for Star Wars: The Old Republic (in other words, if you want to buy it online and download it, you’ll do so through Origin) that does not mean that Origin is required for you to access or play The Old Republic.
Origin is a digital storefront, and the desktop application is there to give you quick access to Origin exclusives and deals.
However, you won’t need to launch the Origin application to run The Old Republic, nor will you patch the game via Origin. Once the game is on your hard disk, you’ll be connecting to our servers to patch and launch the game, and Origin does not have to be running to do that.
To answer another question – boxed versions of the game will include the client on DVD(s)
This is a good thing. I know it would have really pissed off lots of players (including myself) if Origin was required to run a copy of The Old Republic if it was purchased through Origin.