It should not in theory but in reality, it probably does as do nearly all variable powered scopes. Now the question is if it changes enough for you to tell with your shooting ability and the quality of the rifle and ammo.
The upper end scopes are so consistant over different power settings that it could be extremely hard to tell any difference even with the best rifles and best marksmen.
Some lower priced scopes will give you a noticable shift in POI with any power change. Its easy to find out, shoot a group at 100 yards on 24x and then on 10x and see.
To give you a more accurate idea, back up to 300 or 400 yards and do the same, it may suprise you how much in fact the POI does shift.
Kirby Allen(50)