Yes if he knows everyone's names (but will take him some time to write all of them)

Provided he has enough ink.

He'd probably die before he gets to finish wiping off people from Earth because y'know, babies spawning every day.

No.

1. He doesn't have the names of all humans

2. He doesn't have the time to write the names of all humans

3. He doesn't have the material or space in the death note itself to write all the nam

Just kill off the Leaders and Smart ppl and sit back and watch Humanity tear itself apart and then write the names of those that remain.

Deep down, Humans are BEASTS that are only restrained by Reason, Society, and Law and Order. Take that away, and they will return to the BEAST that they really are.