Depends on the school. My undergrad allowed it, but where I teach now doesn’t.
Other than research or working at NASA or something, I can’t think of too many jobs where hiring a child prodigy would be a benefit over a regular smart person. Maybe a quant guy at an investment bank. Top strategy consulting firms like McKinsey or BCG like hiring people with extraordinary academic backgrounds but I would think that a prodigy would get bored making 2x2 matrixes and such.