Is it possible to wake my MBP via Magic Packets from power down? I read Is there a way to power up a Mac Mini remotely?, but that does not seem to work from power down. "Wake for network access" in "Energy Saver" prefpane is ticked.
No - the only (recent) hardware that had Lights out Management (LOM) is the now discontinued Xserve. You will need separate hardware to control the power in response to WOL packets (or other signals) to start the current line up of macs from a powered down state.
Apple's current implementation is focused on sleep. The macs need to - first boot up as they leave the network interfaces listening to wake from only from sleep. Powering down the mac turns off all power to the network interfaces.