I'm not positive, but I am pretty sure the CPU is inactive when powered down, and has little to no activity even during standby. The bios is what handles the power on/off requests, otherwise you would have to flip the switch on the power supply if your OS locked up.
Well it's been a number of years since I designed a PC but I am fairly certain that the processor core power stays on at all times unless you physically separate the plug from the wall. Also unless I'm totally confused the bios is basically processor boot code resident in ROM that the processor executes on powerup and therefore has no ability to do anything on it's own. There could possibly be hardware in the chipset that handles the power on request but I still believe the processor handles that directly.
As far as my attitudes about PC's they're fairly well known at least on the GC2 forum although from what I've heard this OTF is shared with 3 sites at least. Anyway I view a PC as a "personal computer" and basically want mine to sit there like a lump until I specifically ask it to do something. I hate task scheduler and so disable the service. Likewise with automatic updates and the like. I have very tight control on what I allow to execute on my machine. My normal operating services are limited to 17 which include 2 services for AV and firewall along with an open browser.
I basically am very disappointed with the state of the OS and software in general. As a hardware engineer I’ve seen processor speeds, memory and disk speeds improve by literally an order of 1000 yet in the same amount of time I’ve seen most of that hardware improvement be totally wasted by a corresponding decrease in the efficiencies of modern software. Yes we can do more now than we used to but nowhere near 1000 times more. At the absolute best our productivity is 10 times that of 20 years ago. Even that is a gross exaggeration, a more realistic estimate is double or triple. But even allowing for a 10 times net total productivity increase that means that while hardware efficiency has increased by a factor of 1000 that software efficiency has *decreased* by a factor of 100.
Certainly software today is more powerful than that of 20 years ago. There’s obviously no way you’re going to write millions of lines of code equivalent using assembly language but when I used to program (exclusively in assembly) we took pride in tight, clean, well documented code whereas today Microsoft refuses to perform any code optimization whatsoever. Garbage in garbage out.