No. When a phone is powered off, nothing is operational except for the tiny bit that knows to start up when the power button is pressed.
The only way I can imagine this even half working would be to rig up a device that actuates a "finger" (like a hard rubber ball or something else on a motorized lever) when supplied with electricity. Plug that into a wall outlet timer and line it up with your phone so that at the appointed time, the timer activates the mechanical finger, which presses down on the power button on the phone (but not so hard that it damages the phone!), causing the phone to turn on. Not only is this likely not worth the effort to turn on the phone, but you'll still have to enter any security passwords/pin numbers to get into it and make it usable.