Can Kinect data be stored directly onto a USB drive?
Yes. In ROS that would be easily done using bag files. In Windows, however, you might have to look for something native in the Microsoft SDK/OpenNI or code it yourself. Edit: In OpenNI there is something called .oni files for that purpose.
The implicit question: Does Kinect for Windows work in Linux?
As far as I am aware, yes. From what I researched there were compatibility issues with OpenNI initially but they seem to be solved as of May 2012. There are reports of users successfully using K4W in both Windows and Linux there. See this previous question for more info.
I assume the changes have made their way upstream, but the only way to be sure is to test it. If they haven't, you can always use the patched version referred in the link.
My suggestion is get your sensor working in Linux and don't waste your time trying to figure out how to save Kinect data to a USB drive in Windows.