The droid will only stay on if sufficient power has been given to it and it is in either dock mode (or you have the screen always stay on when charging Menu > Settings > Applications > Development > Stay Awake). I used to use my mmdock using the USB adapter to my computer, but as has been mentioned, this is not enough juice to run the phone and charge at the same time. If you run in the mmdock via the wall outlet, the droid screen will stay on. This is also the same behavior for when the droid is in the car dock using the VZW vehicle adapter.
The "launcher" you refer to in the OP is the clock mode with the red background. You'll have weather and multimedia controls right there. If, while you are viewing this clock, you tap on "Select to open launcher," you will see no changes. If you are on any other screen (home, browser, email etc...) and tap "Selection to open launcher," you will be taken directly to the clock.