PaulS:
If you set the pin as an input, and wire it the way you indicate, the LED will only come on when the switch is pressed. In which case the Arduino won't even know anything about the LED.You can't simultaneously use a pin as input and output. One at a time, and the mode can be changed at any time. Just be careful how you wire things.
I said a 'normally closed' momentary button; the LED would be lit when the button is NOT pressed, then turn off when the button IS pressed (then come back on when the button is released, unless the Arduino could in fact tell that the button was hit and then turn off the LED somehow. I'm thinking it could turn the pin to output/HIGH, so there would be 0v between the digital pin and the 5v pin on the other side of the LED?)