Well I think in theory it could happen. I know that my Panasonic plasma TV will shut itself off after a period of time so it doesn't get stuck on an image. The DVD player also has a built in "screensaver".
I can't imagine they would purposefully build an accessory like this knowing it would be an issue. I think it would have to go days on the same screen to get image burn on an LCD.
Sorry to burst your bubbles gentlemen but your statements are not entirely accurate; one of my jobs is testing monitors at a VA hospital for DICOM compliance. It took them several years to decide that monitor power management was worth doing and I failed dozens of monitors for "ghosting." It didn't matter what the monitor was supposed to display, you could see a very distinct but slightly transparent "ghost" of the start bar and some of the icons from the desktop when anything but the desktop was displayed.
Granted, these monitors were left running with the desktop displayed for hours and hours per day for years, but LCD's are not immune to burn-in, ghosting, or whatever you choose to call it.
As soon as they began forcing the screensavers, the problem disappeared, assuming the ghosting was not already apparent. Once the problem occurred, the monitor permanently displayed the ghost image. No new instances of ghosting occurred after the screensaver was activated.
LCD's do suffer from screen burn, but the newer it is the longer it takes to burn in. Perhaps 5 years from now you might have an issue with your droid burning in, but by then you'll probably be using the Droid 3. So really not much of an issue for your cell phone.