The clavicle is the easiest bone in the body to break, but it's generally a minor injury. Worrying about your clavicle as you fall is like worrying about your paint job. A broken clavicle heals readily (unless no medical attention is sought) without much ongoing issue. I learned to fall doing gymnastics and football as a kid, and you definitely use your hands/arms, you just learn to do it without holding them out stiffly, and use your hands/arms to direct the fall. Tucking the chin to chest is key however you're falling.

There is no way that taking enough force in the arm to break the clavicle won't be protective of the head. It's just straightforward physics. Ideally you're using the hand/arm in a way that the fingers/wrist/clav don't break, but that force has to go somewhere. If your helmeted head is taking all the force while the arms/clavicles are protected, then the potential for permanent damage is very real. This is why I wear cycling gloves, so I can use my hands and not have a flash of fear about road rash on my hands.

As noted, many falls are too fast to engage conscious thought. This is why one needs to 'practice falling' mentally, so it's instinctive to tuck the chin and try to roll with it. Also, tensing up is probably not a good idea. More internal joint damage that way. This is why drunks are frequently little injured in car accidents.