If what you want to do it wrap the board into the theme it can be done.
bbPress would be an excellent candidate.
Punbb is also a great candidate.
These two have such simple template systems, that you can modify the css of the board to match your theme, and add the header and footer style to the main indexes.
I would not try to include the WP header, i suggest, once you have the board installed and working, only using the design elements (images, css) of the header and footer to allow them to look identical.
then include your nav bar and add "board" or whatever to the list of links.
As far as i know there are no designers currently offering a theme for WP which includes a message board, or a theme for any messageboard.
I wrote a very basic theme for bbPress (back when it was born, and had no style whatsoever.)
read about that here
hope that helps get you started.