It seems like if you wanted to do this accurately, you'd need to lock exposure to handle a bright blue sky without blowing out -- both aperture and shutter speed. And lock white balance. The question is whether that would allow for sufficient sensitivity at night. But if you're just averaging color values across a section of sky and mainly looking for moon and moonlit clouds, I think it would, since pixel noise will get averaged out and the moon is bright.
For night sky photography with an astro cam you’re still looking at exposure times of 20-60s at night (possibly also increasing the gain at night) and milliseconds during the day. The dynamic range is immense.
As someone who has struggled with this for my own allskycam, it’s extremly difficult to have white balance settings that perform well at all times of the cycle, especially with a camera designed to be more sensitive in the IR part of the spectrum (which will always look unrealistic). Settings that give you lovely white clouds and blue skies during the day tend to give you purple skies and green clouds at night. The quality of light is different so the white balance is different.
You can use autobalance or different white balance profiles for day and night but they each have issues.