Doesn't really help. I want to be able to allow my kids to restart the machine if needed, watch cartoons, play their games, all while the miner is doing its thing in the background.
Vertcoin OCM does this (autostart at login, start minimized to System Tray, start mining automatically), and I've written a small Visual Basic application which does the same for CPU mining (I mine UIS using Yescrypt on Hash refinery with CPUminer-opt). My VB app uses a cmd wrapper to allow easy window manipulation etc.
Awesome Miner already has a System Tray icon, it makes little sense for it to not be able to minimize to System Tray - I just couldn't find the option.
If I understand your request correctly, you simply want to close the Awesome Miner main application so you don't see it in the task bar but only as a system tray icon? Simply click the X-button in the upper right corner to close the main window. This will not exit the application - but leave it running in the background and be accessible via the System Tray icon. Was this the behavior you were looking for?
If you want each mining software console window to be hidden as well, you can configure this in the Properties of the miner, on the Environment tab where you can set the Console window mode.