I know it says that if you overshoot a corner that you can't change lanes upon exiting said corner. My question is can you follow the arrow on the last square of the corner if it offers a lane change upon exiting.
Yup, following the arrows are part of the corner, even the last one out of the corner. But the first space after the corner you enter is the lane you have to stay in for the rest of that move. Not also that in this case, it wouldn't really matter, as you could just change lanes one space earlier and still move to the exact same space.
Just so there is another voice, my interpretation of the rules is that the pictured move is illegal. My club has always played that you can't change lanes when you overshoot a corner. The first space out of the corner is the first overshoot space and so you need to remain in that lane. It also makes the most sense to me. If you are going faster than suggested going through a corner, then changing lanes should be very difficult.