Thank you for the great question. Depending on what type of Hard drive you have this may be possible. Some hard drives give you the ability to back up what you are doing on a PC wirelessly without ever having to connect to the computer. I will post a link to one of hundreds of these devices that will allow the application you are looking for. The link will be below.
With these applications you would need the Slingbox plugged directly into the hard drive (via USB 2.0) and than have the computer wirelessly backed up on the hard drive "cloud" system.
Hope this helps,
Sling Moderation Team