just a silly doubt about glowing an LED
What will happen is you will damage your LED and/or your Arduino since you haven't mentioned a current-limiting resistor (220 ohms could well be suitable).

However the general concept is perfectly sound. You could, for example, have two LEDs, wired in opposite directions. By bringing one pin LOW and the other HIGH, one LED would light up, and by reversing the output to the pins the other LED would light up. If both pins were either HIGH or LOW then neither LED would light up, as there would be no voltage difference between the leads.

There is a calculator for LED resistors.