Yes you can use drupal for a one page site. But Drupal was not made for that - it`s a very powerful and weightful. There are plenty of other lightweight cms you might use for this purposes.
The advantages could be if you had not worked with any other cms or/and want to use drupal flexebility and possibilities.
The disadvantages were mentioned: you could hardly achieve a fast page load, even if this would be the only page on your site and without any unneeded modules enabled.
I would prefer any of javscript mvc frameworks to make a one page application. It would work lightning fast.