When you shutdown Windows, the pc is Not 'Off' as such. The psu is still active, but in Standby mode. This does 2 things. First is it supplies power to the USB ports, if enabled (default is enabled), and the second and more important is that it supplies uninterrupted power to the CMOS chip, which contains all the bios settings and equipment lists and startup procedures etc.
The CMOS battery is almost never used. Which is why the stupid things last for so many years. The only time the CMOS battery is ever activated is in the instant that power from the psu is ever interrupted. That includes turning off the psu switch.
So No, it's perfectly safe to unplug the pc, disable the psu with the manual switch After a complete Windows Shutdown, however, you will then be relying on the battery 100% of the amount of time the psu is disengaged from power.
Your motherboard CMOS battery will go from years of life, maybe 6-8 years or so, to a matter of months, depending on the amount of time it's disengaged and frequency.
A half-dead CMOS battery can and will cause multiple issues, the least of which being that date codes will be changed, which creates conflicts when the last known good bios was saved by you yesterday, but according to the pc it was January 1st, 12:01pm in 1996 or whatever the bios decides is the default Start time.
So there are arguments both sides, valid. CMOS batteries are not rechargeable, so while relying on one for an overnight unplug is fine, just realize that reliance comes at a cost.