If you really want to build something similar, it is possible.
This will give you basic functionality, provide a good learning experience, and is not too difficult.
You will need a WiFi module for the RPi. I regularly use item 24688 from dx.com. There are more beautiful ones, but this is guaranteed to work with Linux. This module does not support MASTER mode, so you will need something else to provide the WiFi network in your house.
You will need to add a lot of storage to the RPi. This will probably be a large flash drive or a USB-connected hard disk with its own power supply.
You will need to install samba on the RPi to allow external access to the files. As an example look at http://www.unixmen.com/standal.....n-squeeze/
This will need to changed slightly for the RPi, but not by much.
You will need a samba client on your phone. I recommend FileExpert for an Android phone.
The end result... You will be able to copy files between your phone and the hard disk on the RPi. This is useful, but does not have a beautiful user interface. Also, this does not provide a sync from the RPi to a cloud service.
So this is something you can try when you get your hands on an RPi.
Does anybody think this would be useful to put as a sample project on the wiki?