You can not use the contact form to send e-mail advertisement
The contact form does not give you any email address. Thus, due to a technical limitation, you are not able to put such an address down in your mailing list. And here the legal problem starts: Under CANSPAM the e-mail address is the only thing the user needs to offer as the identifier to stop receiving any e-mails.
Since you can not put any address down in a mailing list, you can not implement a functioning unsubscribe link. Since you can not implement a functioning unsubscribe link, you can not fulfill the requirement of CAN-SPAM. Since you can not obey the law, you can not send advertisements via the form legally.
§ 316.5 Prohibition on charging a fee or imposing other requirements on recipients who wish to opt out.
Neither a sender nor any person acting on behalf of a sender may require that any recipient pay any fee, provide any information other than the recipient's electronic mail address and opt-out preferences, or take any other steps except sending a reply electronic mail message or visiting a single Internet Web page, in order to:
(a) Use a return electronic mail address or other Internet-based mechanism, required by 15 U.S.C. 7704(a)(3), to submit a request not to receive future commercial electronic mail messages from a sender; or
(b) Have such a request honored as required by 15 U.S.C. 7704(a)(3)(B) and (a)(4).