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

For IMAP accounts we instead only synchronize email headers - this way you have an overview of all your messages but the synchronization is more efficient and the downloaded data does not 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 image - those are then downloaded only once requested. Unfortunately, the bodies of the messages are downloaded automatically, by the nature of the Exchange protocol.