I pretty much assume that Aragorn and Arwen were getting it on way before the fall of Sauron. This goes for both books and movies; though I hesitated for some time as to whether or not my theory applied to the books, Tolkien being so stuffy in certain regards.
But in the end, it made sense to me. Most Elves bond and mate for life; once the mate is chosen, a life-long commitment is usually the result. It makes sense why Aragorn and Arwen wouldn't want to make it public and official for a long time, the situation in the world being so volatile, but I think that in private they were as good as married.
I ultimately don't think it matters all that much, though. Tolkien didn't want to be too specific about the full nature of Aragorn and Arwen's relationship, neither did Peter Jackson. A lot of people see it differently, and I don't feel a burning need to prove my point to them. I think speculation is what makes the whole thing more fun.
alatar, you mentioned how background can affect interpretation, and I agree.