Does the JavaMail API provided disconnected support?
JavaMail provides disconnected support for both IMAP and POP3 in a similar fashion: access to the messages on the mail server is provided, as is the ability to identify different instances of a single message across separate connections to the mail store (using the message's UID). You can also get providers, such as the ones for mbox and mh, which let you store messages on local filesystems.
That's all that JavaMail itself gives you. When it comes to other operations, such as copying messages from the server to the local machine and synchronizing the server and local copies of the mailboxes, the work is left to the applications.
Given this information, the question of whether or not the JavaMail API actually provides disconnected support is up to the interpretation of the individual. :)