Actually, brass that has been exposed to the elements after firing won't be processed by the ammo suppliers we use. Atlanta Arms and Georgia Arms won't take it for reloading purposes...
Whether or not you do it at home is up to you
There is wet as in dew from the grass or cleaning (ultrasonic cleaner, steel pin tumbler, soap & water agitation), and then there is wet that involves galvanic corrosion (found it in a lake, the tin bucket out back filled up with rain, etc) where you have pitting and oxidation. The former is not an issue, the latter may or may not yield good brass after cleaning, but you won't know until inspection.
Some polishing systems use "wet" media, most use dry. I polish all my brass before reloading to clean and dry it. I loathe scratching from grit on my reloads! It plugs the dies too. Water does not damage brass, except after the long exposure.
I've been using the RCBS Sidewinder case tumbler for like 20 years, with the RCBS wet cleaning media. Basically just a concentrate you mix with water, fill the tumbler and let it roll baby. Does a great job cleaning cases, and can be used multiple times over if you filter it after each use. I dry the cases in the sun on a large aluminum sheet in the summer, or in an oven during the winter. No problems with the cases over all this time.