Hi Evan @Evan.meiskin
As already reported in this forum, it is not a problem with harps that have plastic or metal combs.
However, harps (such as your crossover) that have wood or other organic material combs should not be soaked because the comb can absorb water (even through microscopic cracks in the sealant) that can swell and even damage the comb.
My personal preference for such harps is too remove the reed plates from the comb and wash/soak in warm water with a drop or two of dishwashing soap. Then rinse well with pure warm water.
I have also posted here about the advantages of using cheap ultrasonic jewelry cleaners to really remove junk from hard to reach places without any risk to the reeds.
Regards,
– Slim 