Yes. No.
Longer explanation: encryption has nothing to do with authentication and authentication has little to do with the sending E-Mail address.
Encryption is scrambling data with something only the receiving side can decrypt. The sending server contacts the receiving server and asks "hey, can you give me your certificate (or something else) so I can encrypt the data I want to send you?", then the receiving server answers with "yes, here you are" and sends over whatever it is the sending server has to use to encrypt. The receiving server (and only the receiving server) then has a corresponding private key to decrypt the data, that private key stays on the receiving server.
Authentication is sending over a username and password (or other means of authentication), the receiving server checks if that username and password are allowed to connect in the first place. Only when the connection is authenticated you might be able to connect from outside and send E-Mails to other users outside that receiving server. Your E-Mail client does that all the time when you send E-Mails and you can set it up to send either unencrypted or encrypted, depending on the requirements of your provider (=receiving server) as well.
Theoretically you can set up your E-Mail client to authenticate with your username (E-Mail address) and password, but a completely different display name. If the receiving server doesn't check that display name the receiver could show your E-Mail as being sent from me or any other E-Mail address.
You can set up a receiving server to accept anonymous (
non-authenticated) connections as well, but those are usually set up in a way you can only send E-Mails sent via those connections to
internal users. For example: a mail server which hosts finalgear.com mail addresses accepts incoming mails directed to finalgear.com addresses, but not to microsoft.com addresses, unless the sending server provided a valid username/password combination. Otherwise the server would be an
open mail relay so people could connect anonymously from outside and send E-Mails to other users outside that E-Mail system.
The "mail from" field is (kind of) required though so even if a non-authenticated connection is used there is a sending E-Mail address.