I haven’t heard of search engines paying attention to HTML5 tags yet, nor of any screen readers with HTML5 support.
But if/when screen readers do support HTML5, the new document outlining rules should make it easier for users to navigate HTML5 documents that use the sectioning and heading elements.
Companies that make screen readers might be waiting for there to be more HTML5 pages before implementing HTML5 support. It could be a chicken-and-egg problem.
Of course, there are new tags in HTML5 other than <header>
that offer advantages unrelated to search engines and screen readers, e.g.
<canvas>
(you get a 2D drawing surface, for like graphs and stuff)
<video>
(you get to use videos without having to use a Flash video player)