If the trajectory and the damage done by the bullet is such that the parts of the brain involved in pain sensation are quickly and completely destroyed; then theoretically at least, death is likely to precede perception and processing of any pain. However, if this is not the case, death may be slow and painful.
Since there is no means to shoot the brain without penetrating other structures, there is no way to prove a scientific answer. I agree with Adejoke and Olakunie. If the brain is destroyed at a rate faster than the speed of sound, then there is no way to relay the pain sensation before death ensues. If one believes in a merciful God, one would expect the spirit to depart prior to the experience's end, therefore we must explore the metaphysical. In James Blanchard Cisneros' book "You Have Chosen to Remember: A Journey from Perception to Knowledge" he explores the spirit paradigm in which the spirit moves on prior to a person hitting the ground when jumping from a high rise building. Just one possibility....
I disagree to the statement that shooting in the head can be considered as a good method for people who want to have euthanasias, because of two main reason.
First of all, the ball of the gun must pass throw skin so it surly makes pain.
secondly, methods to exam the mentioned hypothesis face a lot of limitation.
Because of the mentioned reasons, I stand behind of my opinion.