Like many others, I did some martial arts training and learned to fall ... but on a bike, stuff happens so fast there is not always time for the simplest, quickest maneuver.

I used to ride flat pedals and with those, I could dive and roll pretty well---I would launch myself off the bike often, and generally managed to land well. (I have actually dived over a car's hood and fender, and over a bumper onto the hood in another accident---in both cases, likely either saving my life or saving myself from great injury.)

On one occasion my speed was simply too great and I got a separated shoulder---at certain force levels, only 1000 % perfect technique will work, and even then, it only mitigates the impact.

Now I ride clipped in, and I find I have a lot less roll ability. The last time I went down hard, I did twist to take the impact on the back of my shoulder (hands in) and even so, I broke my clavicle (collarbone, for those who prefer (even though I hit flat with the back of my shoulder--the force was sufficient to snap the bone up front)) and also smacked the side of my head. Had I put my hand out, I might have had worse injuries ... or not. Doesn't matter, because it happened so fast I didn't have time to extend an arm even if I had wanted to.

Theory is great. In practice, I find that knowing how to fall is mildly helpful, but the idea that people who have learned to fall always come out better ... chance plays as much a part as anything else.

One last thing---as to extending an arm or not, there is no proof that in Every situation, a certain course of action will result in fewer or more injuries, or more or less severe injuries. We can all pretend to know, based on a very small sample data collected from totally unrelated accidents ... but no one is going to stage a hundred identical bike wrecks to test which works better ... and even then, on the road your collision won't exactly mimic the test so why bother?

The one thing I could recommend---if one has time---would be to try to ht with the back of the hand instead of the palm ... hitting with the palm breaks the wrist, maybe the forearm, and maybe the collarbone. If one can hit with the back of the hand and roll onto the wrist and tuck the arm in, it might mitigate the impact without breaking any bones ... but again, every accident is different, and sometimes the only thing to do is pick up yourself and your bike after it is all over, and assess the damage.