I could see where something could shutdown the phone when it isn't charging ie. the PC turns off. But, to come back up. It would need a wake on lan triggered by the PC starting up. However, I don't know if that is possible.
I have been looking at Trigone Remote System Monitor and ModBros online. I did actually setup ModBros on my phone and PC. I like that you can create the layout on the PC and it shows up on the phone in realtime. So, it is easy to move things around and config it how you like it. But, it is earlier in development than Remote System Monitor. I have also read in two comments now for Remote System Monitor saying that if you donate to them it will unlock an advanced feature that will turn it on and off with your PC. Although seems that it would have to be the screen and not the phone. But, I haven't been able to clarify that by reading yet.