In regards to piercing plate, there's lots of variables - range, draw weight, arrow quality, steel quality, and for historical armor - where it actually hits the plate. We have "uniform" armor for the most part - a 16 gauge breastplate is 16 gauge everywhere. Historically, it was pounded from blocks, and thick in vital spots, and thinner elsewhere. A single piece breastplate can be 14 gauge in the front and thin out as much as 20 or 22 gauge at the sides. Then you have to account for angles - you need a pretty good angle to hit plate enough to try to pierce, instead of deflecting. Some historical breastplates have "proof marks", where they would shoot it to show that it was bullet "proof".
Is it historically plausible? Under the ideal conditions of all variables, I would say yes, but did it happen frequently? I'd say no.