Possible a bit late for you but, absolutely is the answer. I have had a site like this for ages (but I'm now integrating the look and feel of the two so I won't link to it).
A suggested file structure might be . . .
If the website is already using header.php, index.php and footer.php for the existing pages, you could change
- index.php to page.php (pages will automatically use this template)
- header.php to header-page.php (change the call in page.php to get_header('page');
- footer.php to footer-page.php (change the call in page.php to get_footer('page');
Then just create a new index.php, header.php and footer.php. You could also create a new style.css and just hardcode the url into the header.