Part of me thinks there was a narrow chance of a woman being elected president in the 40s with Frances Perkins becoming VP and succeeding Roosevelt. She was obviously close to him being one of the few people to last his entire presidency.
Keep in mind that the scenario is asking if a woman could be elected outright. The post-World War II purge of the rosies- and the insistence throughout the war that women's gains were temporary- makes me doubt that she's taken seriously. If she falls into the job like you suggest, she's seen as a caretaker until the next election, which itself would be a testament to the progress made by that first waver generation of suffragist activists.