It's easy to copy a folder in a batch file.
@echo off
set src_folder = c:\whatever\*.*
set dst_folder = c:\foo
xcopy /S/E/U %src_folder% %dst_folder%
And you can add that batch file to your Windows login script pretty easily (assuming you have admin rights on the machine). Just go to the "User Manager" control panel, choose properties for your user, choose profile and set a logon script.
How you get to the user manager control panel depends on which version of Windows you run. But right clicking on My Computer and choosing manage and then choosing Local users and groups works for most versions.
The only sticky bit is "when the folder is updated". This sounds like a folder watcher, which you can't do in a batch file, but you can do pretty easily with .NET.