Absolutely not. Anything in the wall has to be approved for in wall use and no regular power cable is. The risk is if what you do does catch fire, that part is not an acceptable use and if it can be proven, your insurance company will completely deny you any coverage due to the improper use.
If you want to go in wall you need to hire an electrician or go get a permit to do it yourself and extend wall power up to where your TV is using the proper materials. If you need something else in-between, it might be easier to use a painted on wall track to get to the TV from the other unit.
"Don't touch that, this isn't your house and that isn't your tv!" she says.
"But look at it, the contrast is completely blown out, the color is all off and that tint. This will only take a sec..."