BillO:
This might be possible with a true Uno or 100% compatible Uno clone. They work as HIDs. But I think you may have to do some coding to get the SD card to appear as removable storage. But seeing as how you can just put the SD card into most computers made since 2006, why would you want to do this?
Unos don't work as HID. And in this instance, the SD Card isn't easily accessible to pull out every time it needs to have a new set of instructions downloaded on it. So if I can have the device show up as a mass storage, that would be a better solution.