Yes, ultrasonic 'sonar/radar' is feasible. You should do some tests to monitor the sound profile of equipment in the area. There may be interfering sounds coming from known or unknown sources (that is, at a frequency which we can't hear). You want your system to operate in an unused band of the sound spectrum, or have a different pulse frequency, etc. You want to prevent false triggers of your sensor.
Are you thinking of a continual ultrasonic beam? There was an intersection where I believe they put an ultrasonic vehicle detector. When I walked in front of it, I felt a very high pitched, very loud 'sound' in my head. Again, you may want to try some tests.