Hi, I'd like to help you with your question.
Yes, it is possible that a person who has just had a severe injury to experience shock and therefore reduced mental capacity. It takes the mind time to adjust to the threat to the body (or mind itself in the case of mental trauma). For example, when someone is in a car accident, they are often unable to recall the details of the accident clearly. They will say things like "it happened so fast". It is because the mind cannot process the danger and blocks out the more frightening details.
There is a difference between the shock of a severe trauma and a shock such as an accident you can walk away from. A severe trauma, such as soldiers experience in a war, can result in Post Traumatic Stress Syndrome. This is where the trauma starts to affect a person's everyday life through nightmares, fears, startle responses and memory block. In these types of reactions, the person usually needs therapy to manage and possibly medication.
The other type of shock, such as falling down stairs like you experienced, can result in temporary memory blocking. You may have a few hours where you cannot recall what happened and your mind takes the time to adjust and get used to the incident. After you have time to recover, you still may not remember exact details but overall you have a good idea of what happened.
You are able to process things and hear what is being said to you during this time, but your overall mental capacity is diminished until you are able to process the accident.
I hope this has helped you,