I don't have time at the moment to double-check zeus46's calculation, but it wouldn't surprise me if a minute amount could generate that kind of activity.
But the MFMP detector isn't that sensitive, so the particle would have to be bigger, probably by several orders of magnitude.
The normal background with my scintillometer is 80-350 CPS, (basalt - granite background, [typical non-organic soil about 180-220 CPS]) whereas the MFMP device has a much lower background. And I am sure mine misses a lot of counts.
Edit: I haven't stuck mine in a Pb cave, though, thinking about it some more.