[IKE]

20X15,000rpm/60(sec/min)=5,000Hz. (I forget the 60 all the time).

I checked the response on the non contact sensors I was talking about and they are also 20kHz. With some conditioning, you would be able to get a statistical distribution and a minimum clearance, but there is a good chance it wouldn't work well.
You may want to contact a company called LMS International. I know they do a lot of NVH work with the Aerospace industry. Maybe they have encountered a need for measuring something like this before.