First time I fell on the day I started using clipless, I made the mistake of instinctively holding out my hands to cushion my fall. Fortunately nothing bad happened except for the road rash on the palm of my hands, scratches on the handlebar and the brake/hoods/shifter being knocked out of alignment.
Second time I started falling (completely my fault; I thought I might try to learn track-standing, without adequate distance to something to grab onto) my first instinct was "protect the handlebars!!!"