Sure, change:
Code:
$referals = $DB_site->query_first("SELECT COUNT(*) AS referals FROM user WHERE referrerid='$bbuserinfo[userid]'");
to:
Code:
$referals = $DB_site->query_first("SELECT COUNT(*) AS referals FROM user WHERE referrerid='$bbuserinfo[userid]' AND posts>'Y'");
Change Y to the minimum amount of posts the referred member must have. (And maybe note that in the error template so they won't scream "It's broken!"

)