Yes, that's possible. Just copy the contents of Geeklog's public_html folder into a directory on your site. The rest of the Geeklog files should be outside of your document root (i.e. such that they can not be accessed via a URL).
Then you only need to set up $_CONF['path_html'] such that it points to your subdirectory and $_CONF['path'] such that it points to where the config.php is.
bye, Dirk