Yes, research has suggested that a number of smaller collisions can cause damage even if a player never suffers an actual concussion. A helmet also only protects you from external trauma. It acts as a second skull. But the problem isn't always from external trauma. If you are moving at speed and you are put to an immediate stop due to a collision with another player, your entire body experiences a lot of force. Your brain will end up colliding with the inside of your skull due to inertia regardless of whether you were hit in the head or not. That is why simply cutting headshots out of the game or removing helmets won't be enough to protect players. It really gets down to the fundamental nature of football and the physics of its collisions.