Yes, water and shampoo certainly do get through to your scalp and do clean it - the lace is hardly any barrier to water or air. That is one of its good points - you can still feel the breeze on your scalp.
Afterwards the water just evaporates as it did with your real hair when you had it, although it takes fractionally longer (maybe 10 minutes longer?) to dry completely. The lace fibres themselves don't soak water up - they are some kind of manmade fibre - but I suppose water can lurk in the holes and under the threads for a few extra minutes.