Apparently, you must add it as a Send As email on the account where the alias is defined. This must be done even if you are going to use a separate account to email from this address. This is exactly the same behavior as sending from a plus address.
For the authentication, you should use:
Email: Your alias (e.g. alias@example.com)
Username: Your email address (e.g. user@example.com). Note: this is different from using a plus address in that you cannot use the alias as the username, you must use the real email address.
Password: Your email address' password