Waking Arduino from sleep with an ultrasonic sensor
In order to make the ultrasonic sensor work, the Arduino has to run some code to control it.  So it won't do anything while the Arduino is asleep.  

What you can do is have the Arduino sleep for some reasonable amount of time, wake up and read the sensor, and then go back to sleep.  Maybe wake it up once every few seconds.  Do you really need to react to a car in the lot the millisecond it pulls in?