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When working with sites that clients bring me, this is often one of the changes I make, and I almost always see improved rankings. But I'm also changing many things at once, so I can't say I've isolated and tested this one factor for many years. And during that time, search engines have definitely become more sophisiticated, so it may no longer be as big a factor as it once was.
Zeek
The OP's question involves code not visible with a browser, and whether having a bunch of it preceding the contents of the visible page matters. Like tedster, I think it matters, but not much. Still, because I think it matters even a little, I am in the habit of always trying to get the content of the page as high in the code as possible.
In many categories, top rankings is now a game of inches. I see lots of examples of pages that rank well with tons of code preceeding on-page contents. But in a game of inches, why not give your pages every possible chance to rank as well as they possibly can? Every positive tweak carries with it the potential to raise the ranking of a given page.