I am afraid that this is not allowed. As described in the official acceptable use policy here:
You must comply with the laws and regulations applicable to bulk or commercial email in your jurisdiction. In addition, your bulk or commercial email must meet the following requirements:
- You must have the means to track anonymous complaints; and
- You must not obscure the source of your e-mail in any manner.
- You must post an email address for complaints (such as email@example.com) in a conspicuous place on any website associated with the email, and you must promptly respond to messages sent to that address;
- Your intended recipients have given their consent to receive e-mail via some affirmative means, such as an opt-in procedure, and you can produce the evidence of such consent within 72 hours of receipt of a request by the recipient or DO;
- You must use reasonable means to ensure that the person giving consent is the owner of the e-mail address for which the consent is given;
- You must include the recipient’s e-mail address in the body of the message or in the “TO” line of the e-mail.
- You must honor revocations of consent and notify recipients of the same;
These policies apply to messages sent using the Service, or to messages sent from any System by you or any person on your behalf that directly or indirectly refer the recipient to a site hosted via the Service. In addition, you may not use a third party e-mail service that does not practice similar procedures for all its customers. These requirements apply to distribution lists created by third parties to the same extent as if you created the list.