You'd need to write an entire hardware abstraction layer to do anything useful. There's projects that do this for microcontrollers - eg MicroPython and Espruino.
Yes, it would need support from lower level code. But then, so does C -- many things that an OS needs to do, such as installing interrupt handlers, changing the current page table pointer, jumping into a target process already in progress, etc., are not part of the C standard.
