I did some testing around in a virtual machine and here's the best I could come up with:
1) Right-click the CC4 icon in your tray, choose Preferences, and enable both options: Start ControlCenter on computer startup & Open the main window on ControlCenter startup. Click OK.
2) Right-click the CC4 icon in your tray and choose Close.
3) Create a shortcut to BrCcBoot.exe and put the shortcut on your desktop. Right-click the shortcut, choose Properties, and a /autorun parameter to it. Basically, make the Target line look like this (your actual path might be different): "C:\Program Files (x86)\ControlCenter4\BrCcBoot.exe" /autorun
4) Click OK in the Properties window but do not start up the CC4 application yet.
5) Click your Start button and type in msconfig.exe and run that application. Go to the Startup tab and uncheck the Brother Industries entries: Status Monitor Application & Brother ControlCenter.
6) Reboot your computer. After rebooting, that desktop shortcut you created should launch the app and display the main window. The only caveat is that you will have to exit the application via the CC4 icon and the Close option. If you click the X in the CC4 window, it just closes the window and leaves the process running in the tray. With it running in the tray, running the application from the desktop shortcut doesn't do anything, i.e., it doesn't redisplay the window.
If this method is unacceptable, and you don't mind the CC4 application running in the tray at all times, I could probably write a tiny app that you could launch from a desktop shortcut that would simply display the CC4 window once it's been "closed" to the tray. Does that make sense? Either way, let us know how you want to go from here.