With IMAP and Exchange accounts, the message store is on the server, not in eM Client. That is the way those protocols work.
If you don’t want to access the account, you can disable it. That means just like with webmail, when you close your browser you won’t see the messages, also in eM Client when you remove the connection to the server folders, you won’t see the messages either.
If you don’t want to do that, leave the account enabled, so you can see the messages.
If you don’t want to be connected to the message folders on your server, but you want the account disabled AND you want to still see the messages, you will need to move them to Local Folders before you disconnect from the server folders.