The engine only has a limited coolant passage in the block. It is confined to the upper cylinder section of which the water inlet passage is the lowest point. The last time I had the head off mine I hosed the crusties out with compressed air and cleaned the water pump port in the head. Some of these old cars set for years with nothing or even anti freeze in them with no problems. Anti freeze has corrosion inhibitors in it. If I was going to store one for multiple years, I'd fill the water jacket with oil or leave it as dry as a bone if in the right conditions. Heavy corrosion is a result of hot and humid conditions with no protective coating.
Ford's warehouses were the train cars that carried these engines to the various branch assembly plants. Charles Sorensen mentioned this in his book. Right up till the depression started getting bad in 1931, Ford was cranking out model As to meet the demand. If demand fell off then production fell off as employees were laid off. Ford didn't have stock piles that lasted a long time. Engines were stored at the Rouge till the next rail car was available. Some parts may have gotten pigeon holed for a while at the branch plants but they were used as quickly as they could be connected to the assembly line. Late 1931 was starting to see more lay offs. Even in 1932, Ford was building a lot of vehicles. Just not as many as they would have liked to. Ford cars were still about the best for the price. Not everyone went broke during that time.