Well yes, but they usually rely on traditional storage methods (on disk or via something like NFS shares). Normally they use sharding based on the mailbox name and spread it across multiple storage backends.

The only mailserver before this that stepped away from this methodology as far as I can remember was DBMail, but it suffered from many other issues instead.

Using Blob-store like S3 (with some kind of encryption) combined with a db with metadata makes a lot of sense to me for this application. Alternatively, storing it all in something like MongoDB's ReplicaSet would also be interesting.

Now, if ElasticInbox is the best tool for this is a separate discussion, but this type of architecture sure is compelling.