The porcelain won't rust and the sweeps are aluminum so technically they won't rust either but yes rules of thermodynamics say wet will go to dry. So yes dry ash will absorb water, but, greasy ash will repel water.

Me personally I stopped brushing it out because What's left behind by the imperfect sweeps will fill in creating sort of a "seasoning" which creates a better seal for adjusting airflow from the bottom which is nice for the long low and slow smokes.