I do no believe that is actually possible as you are describing it, but you can achieve much of the same with the following:
Keep your files in sync at all times with a cloud service. Ubuntu comes with Ubuntu One preinstalled and it lets you monitor any folder. Cheap to upgrade the space also.
If you are a dropbox-user, that will also work on Ubuntu!
Ubuntu Software Center Sync
If you open the Ubuntu Software Center and go to
File -> Sync Between Computers
or, use the dash like so:
Press ALT -> Write "sync" -> Profit!
I am not sure if you can automatically sync from the software center, but you can see what items are NOT (and are) installed your computer compared to the other.
I understand that none of these is as simple as you would want it to, but you can get pretty far with these solutions (I use them evere day!)