However, since Arrow deals with social welfare functions which take a profile of preferences as input and outputs a full preference ranking, it really says something about aggregating a set of preferences into a single group preference.

I'm going to nitpick here -- it's possible to write down forms of Arrow's theorem where you do get a single output. Of course, in that case, unlike in the usual formulation, you have to make assumptions about what happens when candidates drop out -- considering what you have as a voting system that yields results for an election among any subset of the candidates, rather than just that particular set of candidates. So it's a less convenient formulation for proving things. Formulated this way, though, the IIA condition actually becomes the thing it's usually paraphrased as -- "If someone other than the winner drops out, the winner stays the same."

Edit: Spelling