Stone, I've been thinking about this problem a bit and researching it on my own (the moon that is). The moon reflects sunlight, and that includes IR. Grant it, it is only a small percentage of what the sun emits, but since IR photography is about capturing IR light reflected from objects, then the moon shouldn't be any different. My impression from astronomy sites is that there is more IR reflected than UV, so in all likelihood you could shoot the moon on IR film without a filter since you wouldn't need to filter out the uv light -- I've done this before with candlelight at night and there is a noticeable difference between regular B&W film and IR film (without filter) in how they render the subject.
This is just an (un?)educated guess as I am not an expert in any way on light or astronomy. If it were me I would shoot a few frames on B&W film and IR film so I could see the differences, if any. In there are none, then you know. (actually, I might try this myself the next time there's a clear full moon night)