I just tried this. I had a pre-recorded track playing from SD and pressed the record button on the side, selected SD card and pressed record. It would record my mic while playing the audio from the SD card. The SD card then has a folder with all inputs in separate tracks.
You can adjust the monitor levels of the audio playing from the SD card so you can turn the main volume down for the SD media playing and turn up a monitor w/ the click (we have in ear so I have monitor A to left ear - click only and monitor B to right ear - with back track and whatever live monitoring the band wants).
So I think it will do what you want (and that is what I want to do also.)
I actually did get this to work as well last night. At first I was having trouble turning the click track off from coming through the main speakers. However after digging around, I found under the tweak mode of the media player, I was able to turn off the main out channel. The other great thing about this, is I stored the click tracks in a folder on the SD card. Then from an iPad our drummer was able to view the tracks, and pick one he wanted played next. That is a pretty sweet feature! To your point, I was also able to record at the same time, minus the click track.