I do that all the time with a 23" LCD display and my early 2011 MBP. The laptop's display is indeed off and the menubar, windows, and such are exclusively on the monitor when the lid is closed. I had the same setup with my older 2008 MBP and used it that way every day, all day.
Apple provides directions to do so, and the newer displays even have a laptop magnetic power connector, so it is fully supported and safe use.
That all said, I would not use the MBP as a table and pile papers or anything on it, nor would I block the vents. As long as it has space all around it for air to pull heat off the metal, you will be just fine.