Yep! On the desktop app, we sync all your folders from your main account. And on iOS, we sync any folders from the last 30 days of emails.
Please note: users who registered with 4th Office before September 2017 will see that all their manually-set folders from their main account have been synced (although these will not contain any emails). Only new emails will be synced into folders – this is due to a significant back-end constraint.