Probably not. OLED screens use less energy the more absolute dark pixel in the screen, and darker anything (can be greyscale or color) consume somewhat less than brighter anything, but greyscale on its own usually don't change how much absolute dark and darker pixels being displayed, unless you also tweak the brightness. Usually, the color filter is applied at the end of the process, so the GPU don't get to skip any calculation.
If it makes you use your device less, then you do save energy a bit.
Doubtful, the screen is still the same, same amount of light is getting projected, same amount of graphics calculations is still happening. If there's any impact it's probably quite low, maybe less than 0.0001%
If it makes you use your device less, then you do save energy a bit.