In the past, this was exactly how it was done. Here's an article on the FBI doing it with an Apple webcam six years ago [0].

Should be noted that was after Apple went to the effort of making a hardware delay to try and force the LED to turn on first, but it was still worked around.

[0] https://www.smh.com.au/technology/researchers-activate-apple...

It doesn't have to be milliseconds. Most of people don't sit and stare on the camera all day. I have multiple displays and turning camera for a second when I am looking at another display - or even the laptop one but concentrating on something on the screen, especially the lower part - would slip my attention very easily. Or I might notice something off with peripheral sight, but it is very inexact and while I turn my head to bring it into the field of sight where I have a good resolution, it could be already gone. Of course, the cover has none of these problems. If it's covered, then it's covered.

No, because the LED doesn't need nearly as much power as the camera. And it takes the camera more than a few miliseconds to start working.

This used to be a thing, where you’d flash the LED briefly and hope the user didn’t notice. But new Macs prevent this by having a minimum duration the light will remain on.