Somebody mock up the boyfriend looking back meme but with the boyfriend as Tarantino, the girlfriend as Sam saying "Po Pay", and the bottom left chick captioned "Toes".
Isn't this just a simple case of "get the moisture away"? Blowing into the dishwasher doesn't move the moist air away, it just moves it around in the box. Blowing out pulls the moist air away from the dishes and out into the room.
If your box fan was pushing dry hot air (like a hair dryer), hot enough to meaningfully speed up evaporation, then blowing in would probably be better.
What is that law of the Internet that says, if a headline ends with a question the answer is always "no".?