Yes, I've just done this and it switched off completely !
But how is it possible ?
How much current takes the LCD and its backligth on the Arduino pin when the VDD 5V is off ?
Can it destroy the Arduino taking too much current on its pin. I guess it could because the voltage was falling down 3.5V in that case and even more when I unplugged some of D4-D7 or RS, EN to make some test !
Quite scarry !
Is it normal ?