The Notes feature @cyberzork outlined is a folder with individual notes but they are not linked to an email message. I think the original poster is referring to email notes, as outlined here: Offload your thoughts with notes for email | eM Client
Email linked notes according to the blog page is only synchronized when using an Exchange account, not an IMAP account. As the original poster says, since IMAP doesn’t support notes such as these being synchronized server side, one option would be to use a secondary sync service just for the notes to sync (which in @olley olley case was accomplished through a secondary service plug-in). As mentioned, for this to be included in eM Client in that same way would be a big task because of the additional infrastructure, and probably not a preferred method anyway since it means your data is stored across multiple providers.
I think one possible work-around (hack) solution for IMAP would be to store the notes in an IMAP folder as separate emails, which could then be linked back to the original email that the note was set on. This wouldn’t require an additional server, and thus much easier to implement. The difficult part would be linking the two, especially if the IMAP server changes the UID on the message where the note was set on. So it is a possible work around that maybe @Gary would have more input on if it is realistic, and worth putting on the sleekplan voting system or not. I admit this is a feature I would like to see myself, since having the email notes only locally is very limited.
But currently if you want to use eM Client and require email linked notes to be synchronized server-side, then you must use an Exchange server side account according to the blog post about this exact feature.
More forum discussion about the email notes feature at: Question about notes - #6 by itsec