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<h1><img src="blah" alt="my header"></h1>
In Opera, with images disabled, 'my header' renders with the style of h1. I'm personally hoping that SE's do something similar!
It's pretty easy business to extract the text, and treat is as a header. My guess is the good search engines are starting to actually parse the pages (with tehoma talking about context), rather than just scan for tags and keywords. Which means that this trick would work.
Fingers crossed.
A search engine will see and index nothing there other than a stock alt tag. (I've played with every variation of that on earth). Tedster is right Alex, the title tag is your friend:
<h1><img src="blah" alt="my header" title="my keyword one a two and a three"></h1>
The title tag is getting more weight than the alt tag these days. Alta is the only I know that is really giving it anything at all. Google will use alt's when all else fails, but I don't think they work into the algo at all (counter opinions?).