Comment by perilunar
Not really. The Earth still revolves once a day, and goes around the Sun once a year, and the Moon still goes around the Earth once a month. We can change the way we divide these periods but the periods themselves are fundamentally physical.
Example: https://sunclock.net/#calendar
The weekends and month names/dividers are ‘artificial’, but all the other lines — the days, moon phases, the equinoxes, solstices, apsides — are natural.
And the reality is that there is not many actually sensible ways to divide they number of days in year. 12 is pretty much best we can do. And being highly divisible it does work very nicely... So even without moon, it is one of the better options.