Depends if the TV has the option to turn on after a power restore. You can test this easy, just turn on the TV, unplug it and then plug it back in and see if it turn on by itself. Most newer CRT's have this option. If it doesn't turn on by itself. trying turning it on while holding the power button in, if it stays on, then unplug it and plug it back in while still holding the button. If it turns on then all you have to do is wedge something to keep the power button pressed.
Assuming that your have figured this out, and your simple question is if the smart strip will send power to the tv, yes it will. THe smart strip I have has one MAIN outlet, a few switched outlets and a couple "always on" outlets.
The MAIN outlet controls the switch outlet. THe smart strip measures the current flow on this outlet, and when it detects an increase, it powers on the switched outlets, when it senses a decrease, it powers the switched outlets on. You plug your PC into the MAIN, your TV, speakers, marquee, powered USB hub, whatever into the switched outlets. When you turn on your pc, everything else turns on, when you turn your pC off, everything shuts off. Then all you do is extend your power button on you pc to wherever you want on the cab. All you need is a standard NO momentary switch. I have a regular arcade button turn my stuff on and off.