Yah, personality screening is one of the questions we do on the questionnaire we use. It's the last question; "How patient / nice was the caller in answering the preceding questions? How nice did they seem over the phone?" Then I have them rate the caller's kindness / patience on a scale of 1-5.
The response that is written in that box often can decide whether I want to go give a bid or not. If they were rude and impatient and asking, "What's with all the questions??" or "How long is this going to take? I need to get back to work!" then this is someone who is definitely a little too high strung and I'm not too interested.