Simple answer: No, it would not. Even if you would use Diffie Hellman key exchange on elliptic curves along with AES encryption, it would not.
There can be the man in the middle attack, where someone will get in the middle of client and server, and read all data, and just forward them. Like this, you CAN bypass even Diffie Hellman key exchange.
That is way why SSL is here, since once you have SSL cert, then no one can really decrypt the communication, and your server is identified by the cert (so I can no create a fake server, as I would not have the certificate).
Also question: What do you want to secure? Make sure that other client does not send you a message as someone else? If so, then socket connection has a unique ID, therefore, you as the server can identify who sent you the message. (as far as I know)