I can't tell you about that drive in particular, but here's my experience with the CCK:
I have the USB to lightning version of the CCK, which is what I assume you're referring to. I have been able to transfer content to my iPhone from an old Imation 8GB thumb drive, and I regularly use it with a Targus SD card reader to transfer from SD cards (rather than buy the SD card version as well). I have other thumb drives that do NOT work with it, as they appear to draw too much power. (I seem to recall hearing that the new max current limit is 20mA -- not exactly sure.)
Whether on SD card or USB drive, your content must be in a DCIM folder at the root. No subdirectories. And you can only transfer one way.
The filenames themselves must be exactly 8 characters long, with exactly 3 character extension. And, I believe the extension must be in the set of photo media extensions (.jpg, .mov, .mp4, etc.), but not sure of this.
In this way, I have copied .mp4 movies to my iPad for viewing, but was then stuck with the playing back the movie in the Photos app, which is not fun. I now have a Sandisk Media Player for this particular purpose. I think there are similar wireless devices you can use with your hard drive to serve up movies, etc. that could be more flexible.