All though your a newbie by the looks of it. Yes you can do that. I really think you should try something before asking someone to make sure you can actually do it.
ID also change this
if( $first_name == "")
to either if(empty($first_name))
or better yet
if(empty($_POST['first_name']))
or if you are PHP 4.1 or lower
if(empty($HTTP_POST_VARS['first_name']))