Yes but it requires the right size round over bit, aswell it will only work on strat style necks, angled back headstocks would get in the way. I would also recommend the router be mounted in a table instead of hand held. As with any routing operation, this can be very dangerous and damaging if you don't feed the wood the correct direction.
If you have a copy carver then, yes, and you'll just need to smooth it out with some sand paper after
Alternatively, spokeshave is my weapon of choice, but there is also a rasp (like a cheeze gratter for wood), or a stationary sander with the appropriate sanding grit.