Let me see if I understand what you are asking. If the computer is powered down because power is disconnected (not a graceful shutdown) can you wake the computer remotely? On the same computer, if you shut down the computer with normal Windows shutdown, you can wake the computer remotely.
If this is correct, then yes, you should be able to wake the computer that lost power after power is reconnected by sending a magic packet to the MAC address of the computer.
Wake on LAN from power down depends on the power management capabilities of the system and the BIOS, but if you can wake up from graceful power down, you should be able to wake up from power loss after power is restored.
I tested here using WOL Fusion. I had a switch in between the two computers. I pulled the power from my desktop computer. I used the MAC address of the powered down computer in WOL Fusion to wake up the computer.