Gmail now supports third party outbound servers to send mail

Gmail has added suport for third party outbound servers to send emails. So, if your other email provider supports POP and/or IMAP access, you can choose Gmail to send your messages. To switch to this new method, go to the Accounts page under Settings, and click "edit info" from the "Send mail as" section. Then choose the option to "Use your other email provider's SMTP servers."

Find more details at Official Gmail Blog:

Send mail from another address without "on behalf of"