I don't have a definite answer to the question posed in this post's title. That would have to come from Chrysler archives, an automobile restoration expert or perhaps a knowledgeable member of a club devoted to one of the Chrysler Corporation brands active in the 1930s.
My strong suspicion, however, is that the answer is "no," even though various publications in my automobile library state otherwise.
Let's begin with the setting. Chrysler Corporation's 1938 brands (Plymouth, Dodge, DeSoto and Chrysler, in ascending price order) shared a typically rounded, heavy-looking basic body whose style was in line with cars from General Motors and other firms. However, cars such as the Lincoln Zephyr and Cadillac Sixty Special along with the usual Detroit scuttlebutt must have made it clear to Chrysler management that competitors would be offering sleeker designs for the 1939 model year.
Chrysler did plan a total redesign of its line for 1940, but it probably became obvious that its 1939 line had to be freshened to remain competitive until the 1940 cars appeared. So 1939 Chryslers, DeSotos and Dodges were given a truly major facelift, a facelift with plenty of new sheet metal and reworked tops that gave the appearance of a complete redesign. Plymouths were given a less-comprehensive, but still extensive, facelift.
I'll use Plymouth to begin making my case.
One thing that puzzles me is why the Plymouth wasn't facelifted as completely as its senior brothers; after all, Plymouth production amounted to more than 40 percent of the Corporation's total, which would have helped amortize the tooling expenses for the other brands. Perhaps it had to do with Ford's late-1930s practice of having its less-expensive range featuring style characteristics of the previous year's top line. That is, maybe Chrysler was simply following a fad. Or perhaps, because of that fad, they thought they could save tooling expenses on Plymouth and get away with it in the marketplace.