Compare an Arduino with a light bulb. It draws current. If the light bulb (or all light bulbs together) draws too much current, you will blow the fuse in your house. In a similar way, if the Arduino draws more current than the power supply can deliver, it will not work (power supply drops voltage or shuts down).
Be aware that the voltage regulator in the Arduino needs to dissipate the heat caused by the voltage drop (12V minus 5V equals 7V) and the required current (e.g. 100 mA total). It will shut down when it gets too hot.
If you're only powering the Arduino, you will be OK. If you're also powering other 5V devices from the 5V output pin of the Arduino, it might or might not be OK; you will have to sum all the currents of the connected devices.