No in your case, the output is the html source from the file including contact.php. ANYTHING that is sent to the browser before a cookie function will screw it up. Cookies are sent in the headers. session_start() sends a cookie so by having your output go to the browser before your call to session_start(), the cookie can't be sent in the headers.
Check the link in my signature for more.
My helpful sig has gone because a mod below the administrator gave me an infraction - despite the administrator personally agreeing to it.
If you need any php tips or tricks you can PM me.