I don't have a whole lot of experience with Origin (what little I do have was enough to learn that it utterly sucks balls) but as far as I know with the games on offer here you really only ever need to run Origin once to install and activate the game, then never again. That was how it was when my friend gave me a code for The Old Republic (HORRIBLE game!). Unless they changed it anyway. If it's still true though it really shouldn't be enough to stop you from buying a game that doesn't explicitly require Origin to run.
“The greatness of a nation and its moral progress can be judged by the way its animals are treated.” - Mahatma Gandhi