Simple question but searching I can't find much evidence. I use an LED device (not OLED), would that also make a difference?
If the screen is LCD or LED then, there is no battery saving as answered on this question Will grayscale increase or decrease battery consumption? on AskDifferent.
However with an AMOLED screen, there is an advantage as the black pixels will be turned off. According to the article Why You Should Use Always Use Dark Mode on Phones
That said, the differences in power Google discovered between using an app normally and using its "night mode" (or dark mode) were striking, particularly for OLED-based phones. For example, when testing an AMOLED-based Google Pixel, Google found that Google Maps uses 63 percent less power when it Night Mode compared to normal mode. By contrast, an LCD-based iPhone 7 saw no change in power consumption
Although Night mode is not grayscale, the advantage of switching off the dark pixel should help in saving the battery.
No, because power is still being consumed to display the image. Had the device been OLED or AMOLED, then it would have saved a bit of power, since each pixel is an individual source being powered, and black pixels would not receive power.
The best bet on saving power with LED is if the GPU was processing images in 8-bit, but it does not. If you turned on grayscale and took a screenshot then turned it back off, the image is still in color.
For an LCD device the major power factor is the consumption of the background lighting. If you show the screen in color or gray does not have an impact ob the background lighting, therefore it does not make a difference in power consumption.
In OLED displays each pixel is shining, or to be precise each sub-pixel (red-green-blue and sometimes an additional white) is shining requires power. The more pixel and the brighter the pixel shine the more power is required. I would assume that e.g. a blue a sub-pixel shining at 100% requires a bit more power than 3 RBG sub-pixel shining at a lower brightness in grayscale mode. However the effect should be not very high. Therefore I would assume that the saved power by an OLED display in grayscale mode is very small.