I've done this a million times on my desktop computer, along with my laptop. I've never had a problem. I unplug and plug back in the LCD of my laptop on a daily basis because when I close the lid the screen stays on. So I unplug both the display and backlight cables so it doesn't overheat. I haven't had a problem.
The screens themselves still work because they still are displaying the message "No input signal", but may have gotten screwed up somehow. Have you tried resetting both monitors?