Answer

Yes, you would be correct in saying that the goal area delineates the area from which the goalkeeper/defender shall take goal kicks. In the past, the Laws of the Game also stated that certain offences committed against or by the goalkeeper in the goalarea were penalised in a particular way. Thankfully, these offences no longer appear in the Laws, and thus goalkeepers may not enjoy a perceived "protection" due to their status when in the goal area.