Yes, my example centers the mouse every time GetMouseX() or GetMouseY() is called, which is called each time through the loop.
I did notice one problem though. If you have a high mouse sensitivity setting, the movement becomes more coarse. For example, a sensitivity of 4 will cause the mouse to move in groups of 4 pixels at a time. This is because the final mouse movement is calculated as a multiple of the true mouse movement. So the true mouse moves one pixel and the final mouse moves 4 pixels.
I did notice one problem though. If you have a high mouse sensitivity setting, the movement becomes more coarse. For example, a sensitivity of 4 will cause the mouse to move in groups of 4 pixels at a time. This is because the final mouse movement is calculated as a multiple of the true mouse movement. So the true mouse moves one pixel and the final mouse moves 4 pixels.