What then happens is that over a long exposure, the plate will appear to rotate around the guide star.
If the autoguiding system is 'strong' enough (again, using the force analogy), you will still be able to keep the guide star perfectly steady. That is where you need to bump up the loop gain - which can be problematical if the gain is anywhere close to or greater than 1, at which point, the loop will oscillate. If the PA error is large enough, the RA and/or declination error will be too large for autoguiding to compensate for. There is no real force, of course, just that the plate is moving in the RA direction at a rate that is not precisely the sidereal rate, but the plate also moves in declination. What happens when PA is off is that there is a constant error (think of it as 'force' if you like) that is tugging the mount in some direction. as long as the autoguiding can overcome the bias from any PA error. I don't think polar alignment (PA) is the problem.
