yup, it depends on the motherboard.
A good USB keyboard, even wireless/BT should appear to the system as a standard keyboard and conform to the specs for such a device - they can't do additional features until the drivers are loaded, but it should work for basic functions (at least if it's receiver sold with the keyboard such as most of the Logitech sets)
Most motherboards from the past 10 years (near enough) should be able to work with a USB keyboard (they have to really to allow you to set bios options with them), where it can get tricky is between the point of the handing off the PC functions and the OS loading the drivers (which is why sometimes USB keyboards will work in the Bios, but then not work until the OS is fully loaded - and why the bios normally has an option to continue USB keyboard support or hand it over to the OS).
So what it comes down to is the USB and "power on" options in the bios, most motherboards should have an option to continue to power the USB ports when the machine is "shut down" (ATX spec machines never truly power down, they can't and still boot when the "power button" on the front is pressed).
Re the number of keys pressed, that is more down to the controller chip and layout of the electrical connections in the keyboard than whether it's USB or PS2.
Some keyboards use control chips that due to the number of inputs, and layout of the switching on the keyboard might only be able to work with 3-4 simultaneous key presses, or might not like certain combinations being pressed at once, I think that was mainly a problem a few years ago when certain control chips were being used because they were cheaper
