My friends convinced me to try clipless pedals, that I never trusted too much (BMX background). Now while I'm getting used to them and experience very funny falls, I try to figure out, can a used-to-cleats rider drop his foot in a sandy corner, or the only thing he can do is to get used to proper race style cornering?
Yes it is possible and some times necessary. It's best though if you already know the trail you are riding so you can prepare yourself at the right moment. For a classic example see inhow the rider unclips at 1:10 in order to save himself at 1:12.
This of course will work well as long as you've set a moderate tension so you can unclip pretty easily (but not very very easily).
As your pedals age and cleats wear it will get much easier to unclip at a moments notice.
Until then, you can try adjusting the tension of your pedals or do as I did and just ride at slower speeds until more comfortable with cornering while being locked in.
Even with looser clips and experiance I still fall, but that wasn't any different then when I was using flats :)