Gmail allows its users to send emails as though from another email address, as long as that address has been verified. Is doing so possible through Thunderbird and the Gmail SMTP servers?
Yes, as long as the e-mail address is verified in your Gmail account and you are able to send messages from it using Gmail's regular web interface. Just add a new account to Thunderbird with the appropriate name and e-mail address and configure it to use
smtp.gmail.com with your usual credentials.
Note that if you attempt to use a
From: address that hasn't been verified in your Gmail account, Google will automatically change it to your default e-mail address.