Header tags are part of your page copy, as they are visible text for your visitors. While some might consider the alt attributes to be part of your page copy, others won't. They are taken into account by some search engines, but you need to remember that the primary reason for using them is for people with text only browsers, with images turned off, or with accessible browsers that are designed for the visually impaired.

So...make sure your alt tags are clear, consise and accurately describe the image they are attached to and you may experience higher search engine rankings.