@lamp Laptops are designed to be low power, especially with the screen off and no graphical load, so if you are happy with just one small HDD or usb attached HDD's, they're quite suitable for a low power NAS.

NUC's use even less power than a laptop.

The NIC, or ME backdoor needs to support listening for a wake-up packet and the hardware needs to allow the NIC to trigger a poweron to get wake on LAN.