It will damage the Arduino.
You can apply 5V or 6V to Vin.
The Arduino might run at a lower voltage, but that is almost never a problem. The Micro uses the ATmega32u4 which works at 16MHz at 4.5V.
If the Micro doesn't use a lot of power (like 10 leds) you could measure the 5V voltage pin. It should be very close to 5V if Vin is 5V.
A lower voltage will have influence on the analogRead() if the default voltage reference is used.
The schematic of the Micro is on its page, http://arduino.cc/en/Main/ArduinoBoardMicro