The user has the option of storing the entire message in the local system or on the server or both. It is like an interactive session between the client and server where the client asks the server for parts of messages like headers or bodies of certain messages. When using IMAP in online mode, the mails are located in the server, but the mail client does not copy the entire message at once and then delete it from the server. If you decide to only download message headers and mark messages for individual download to Outlook you need to be aware of some limitations.
Ensure that the account is set for downloading complete items including attachments.