Before you delete or modify it you should backup your site via FTP as well as backup its database. That way if deleting the file has negative consequences you can easily restore your WordPress installation to its former state.
Once your site is backed up, I would recommend double-checking your plugin list to be absolutely certain that another caching plugin hasn’t been installed somehow. Once that’s confirmed, you can try deleting the advanced-cache.php file.
Yes. WP Super Cache is only checking for the file’s existence, not its specific contents. If the empty file being there is what’s preventing it from running, deleting it should allow WP Super Cache to work.