Although C15th. armour was very effective (and by the way, all this stuff about 'had to be winched onto horses, couldn't get up if had fallen over &c. &c. is Victorian nonsense), a man who became isolated from his comrades and surrounded by enemies would have no chance of survival. Once immobilised on the ground by force of numbers, opponents could pierce vulnerable points in the armour. There were even special daggers designed expressly for that purpose.
Richard may have lost his helmet in the fray, but there is no chance he would have gone into battle without one.