No because relays can be closed, and usually are. Your ISP's SMTP server requires authentication, using the credentials they gave you, and almost certainly uses TLS also.

Your [email protected] address (or perhaps the me part of it) is used for authenticating, along with the password. It will likely be used as your envelope address when sending; the SMTP command will be MAIL from: [email protected], though there could be flexibility there to accept other sending envelope identities.

In any case, your mail's From: header will have the [email protected].

If the ISP were to filter on the From: addresses after receiving the content of the e-mail, you'd have to negotiate something with them.