No, email synchronization cannot be limited just to a selected time period (for example from only the past few months or years) at this time.

For IMAP accounts, we by default only synchronize the email headers instead - this way you have an overview of all your messages but the synchronization is more efficient and the downloaded data doesn’t take up too much space.

A full message is downloaded into the eM Client database only after you open it.

For EWS accounts we automatically leave out the attachments and images - those are then downloaded only once requested. Unfortunately, the bodies of the messages are downloaded automatically, by the nature of the Exchange protocol.