Is it possible to integrate HTML5 Boilerplate to WordPress theming structure? If anyone got any ideas on how to do this, can you share how or your opinion about this?
Yes it is very possible. How to make it to be WordPress theme? Slicing them to be header, footer, and sidebar. The rest are contents, the content for post, page, custom post, archive, etc. I suggest you to learn WordPress theme development from default WordPress theme, such as twenty ten, twenty eleven, or the recent one, twenty twelve. They are great resource to learn best practice and basic things to be implemented in WordPress theme development. :-)
Oh I forgot to add some useful links to develop WordPress theme. You could search the tutorial of creating WordPress themes everywhere, such as wp.smashingmagazine.com, wp.tutsplus.com, etc. But I recommend you to refer this page first Theme Development on WordPress site official. http://codex.wordpress.org/Theme_Development.
Hope it helps. Cheers!