I have an XBOX One. When you cut the power whether it be unplugging it or cutting power to the outlet, and turn the power on again, it doesn't turn on. You also should shut it down properly each time you turn it off, not merely cut the power.
Also, the off/on signal to the TV, Speakers, Cable Box is sent via IR blaster. NOT Wifi. Wifi and Bluetooth only work when the devices are on. Sending a wifi signal to a device that's has no power will do nothing.
However, in the case of the XBOX it's always on and listening even when you've shut it down, so you can probably send a signal to turn that on via wifi. If the TV is plugged into the XBOX, then it may work.
But again, once you cut the power ( as in with some kind of smart plug), you've turned it off and that won't work. All you'll be doing is turning on the flow of electricity, you'll still have to somehow turn the box on.
At the moment the only remote that I know works with XBOX One AND can be configured with the Echo is the Harmony Hub.
You'll have to work backwards. Find the hub that works with the Echo...probably via IFTTT recipes, and then see if it's compatible with the XBOX.
Or bypass the XBOX and look for an IFTTT recipe that works with your TV brand.