I believe the short answer is no.
Email headers are just text, so if you are using sendmail or something, you can use whatever you want. However, it might (see: will likely) end up in his spam folder.
Gmail needs to protect it's reputation, so they will always add a breadcrumb to say who actually sent the email. For instance, you can setup gmail to send email "from" non-gmail addresses, but the message will be sent from your gmail address "on behalf" of your non-gmail address.