If an attacker can tell which part of the index was modified, that gives them enough information to decrypt the index and e-mails.
Clients would always have to download+upload the full index (which needs to be re-encrypted with a new IV). This is a huge problem - the index can easily be hundreds of MB for a large mailbox.
Technically if a client has a full index version X (in plaintext), it could modify X to get X+1, compute a binary diff between X and (X+1) - encrypt and upload the diff.
Another client on index version X could download the diff, and get index (X+1).
Some desktop client should probably do compaction from time to time.
You would have to re-download the index after compaction. But the index and patches would be independent - you apply the decrypted patches to the decrypted index.
I'm not quite sure what you're getting at. It sounds like you're describing a known-plaintext attack, which modern ciphers are not vulnerable to. And what you are describing makes it seem like full disk encryption would be totally useless, but we know that's not the case.
Clients would always have to download+upload the full index (which needs to be re-encrypted with a new IV). This is a huge problem - the index can easily be hundreds of MB for a large mailbox.