Anything with an open cell structure can hold water.
The idea of water repellence on chopped-wool is to prevent wicking/ capillary action, I believe they spray polybead with same.
What surprises me is the wool cavity bats rely on strand orientation - most likely up/down? In which case what is the betting that some are miss-installed, never mind gaps left which are a more serious known problem re water tracking.
I'd prefer PIR bat in a cavity with air gap to the outer leaf, closed cell, water can still run down the rear of the outer leaf.