Yes, IF it hits it straight on.
But the finer plate armour was angled, as a bad example look at the plate tunic in
UO, it has a sort of ridge that runs down the middle of it. this is also why the hounds skull (also known as pig snout) helmet became popular, because it's snout meant that arrows would glance off it, rather than the great helm which was a round pot helmet with a more flat surface, if that makes sense?
But yes, at short range, if the archer could hit a flat surface the bodkin would go through. at least I'm pretty sure it must have! although there are also accounts of archers aiming (and hitting?!?!?!!!!) the slits in the visors of helmets! that sounds crazy but seems to pop up quite a lot. this was ofcourse only done an extremely close range.