Sure you can do that. You just have to include the appropriate header in the message that you send with JavaMail.
Now, I don't remember what the header is or what its value should be. But you can find out for yourself. Use Outlook to send a message with "read receipt requested" (or whatever its term is) to some e-mail account outside its domain. Then look at the headers in the message (almost all mail clients have a way of doing that). You should recognize it right away.