Yes, that will work using Auto FTP Manager.
You will require 2 automated profiles. The first will download and keep a backup on your local PC and the second profile will upload from your PC to your mirror site. You can use the action rules to transfer new or changed files. Here is more information on setting action rules:
https://www.deskshare.com/help/AFM/ActionRules.aspx
Use the scheduler to execute each transfer profile separately and with enough time in between schedules so that there is no overlap of transfers.