It doesn't work that way. Effectively, the nose of the ship is being pulled up, and the pilots head might follow that movement not immidiately. The result is that the head of the pilot would appear to move down (in relation to the (cockpit of) the ship and then catch up.
Once the head has cought up with the movement (the forces), it would go back to looking straight. But see what happens when you constantly "pull up" your ship: The instruments stay off screen, and that is totally unrealistic.
Pulling up means that the dashboard (instruments) move up and not down, and after a short delay for the head to catch up with it, they would have to move move down to "normal".
The explantion that would conform to physics is that the dashboard would sit loose in that it is mounted on springs. When you constantly pull the ship up, due to the resulting forces these springs would be stretched or compressed as long as they are subjected to this force.
If the pilot is not strong enough to keep his head (or move it back) in position with his muscles alone, the head would move down and stay down. It would not move up and he could he still see the instruments.
What other/all thrusters do in total is in a way irrelevant for this because the ship does turn around an axis that doesn't necessarily go through the ship (from left to right or right to left). Otherwise the ship won't turn. Imagine the ship flying round in a circle, and you will know that the pilots head would move down and not up (unless the pilots default position is sitting with his neck bent backwards all the time, but nobody sits like that).
If the axis goes through the ship, what happens depends on where the pilot is located in relation to the axis. He can sit in front, on it or behind it (Anaconda).
My Anaconda is in storage somewhere so I can't try it. Maybe someone in an Anaconda can verify what happens when they pull up with the ship otherwise standing still (assuming that the pilot is at the rear end of the ship and not at the front). Does the cockpit move down or up?
If it moves down and if the pilot is sitting at the rear, then how would you explain the cockpit moving down (if it does, but I never noticed a cockpit moving up rather than down)?