Yes, but much depends on range, arrow type, and the quality of the plate armor. The heavy English longbows, throwing heavy arrows made of ash and equipped with “pile” arrowheads were known to pierce plate.

Does arrow pierce armor?

Computer analysis by Warsaw University of Technology in 2017 demonstrated that heavy bodkin-point arrows could penetrate typical plate armour of the time at 225 metres (738 ft).

Can arrows pierce chainmail?

Broadhead arrows - definitely, it would. Bodkin arrow - probably yes. It depends on many factors like distance between archer and his target, angle of impact, draw of bow, etc. But even if an arrows penetrates the mail, it will not kill the soldier wearing it.