In order for Marketo to send anyone an email they must exist in your lead database.
I think if you were to stick with your form the way it is you would need to use Soap Api Create lead function to take the email address from your "Friend's Email Address" custom field and create the new lead in Marketo based on that email address, you could then have a trigger campaign set up to send that newly created lead the referral email.
Maketo has a forward to friedn function that runs on the email sent, so maybe you could try to get your leads to refer a friend this way:
http://community.marketo.com/MarketoArticle?id=kA050000000L8IBCA0