Using non-standard mailbox backend - is this even possible?

What I'm trying to do: provide an IMAP server as a facade for standardized e-mail access, without using on-disk mailboxes.

What I have:

• multiple TB of e-mails, stored in MySQL in a completely non-standard format
• a webservice providing access to these e-mails in a structured way (enumerate/create/delete folders, list/read/delete/send messages, etc.)

Currently, users access their e-mails through a web frontend or a smartphone app (both of which query the webservice for data, under the hood). This works; but I now need to provide access to the mails via IMAP as well.

I have been looking at various IMAP servers, and it seems that Dovecot allows for custom storage backends. However, all the examples I have found are using local mailboxes for storage.

What I'm trying to get to is an IMAP server which would query the webservice for folders/messages instead of looking into a local database/mailbox. (Is this even possible, or would I need to somehow fake the existence of a local file structure, e.g. by writing a FUSE module mimicking http://wiki2.dovecot.org/MailboxFormat/Maildir ?)