Short answer: no, you don't need an MTA.
Long answer: an MTA is often referred to as an "smtp server". They're the real backbone of the email system. When you connect to smtp.myisp.net, that server is running an MTA, which connects to another MTA whose address corresponds to the part of the destination email address after the at sign. This MTA then files it somewhere where the recipient can pick it up (whether this be by POP, IMAP, or simply by using a shell on the server).