Pure Hibernation and Shut down are the same from this perspective.
In both cases the computer is totally Off. On Hibernation after start the previous status of the RAM is loaded from a file that was saved on the HD thus the computer comes up faster in the same status that it was before.
That said some manufacturer (especially with Laptop) has "crafty" ideas about Hibernation.
You can also invest few $$$ and get yourself a PCI card that is known to do WOL as it should, and disabled the on board NIC (personalty I do not like the Atheros onboard Giga NICs).