No.
The shadows would make the ceiling look like a slightly different color anyways.
If it saves you money, I don’t think it’s necessary

If your ceilings are nicely painted, and are not dirty, I see no reason to paint any ceilings.

I always like a fresh start in a new to me home so I would do the ceilings in the WD and then you know it is all done.

I agree, if it's clean and the color is fine, I would not go to the expense of painting the ceiling.

if they're in good condition, then basic white is a perfectly fine color. my only exception would be if they were glossy. matte is way better -- it hides imperfections better, and reflects the light in a much nicer way.