Hard to tell. If it were a hundred years on I'd say yes, but in this period they were still coming off the back of a time when insecure or unpreferential candidates could be skipped if it was thought that the country would be threatened with them as monarch (i.e. with a child king unable to exert any power). However, I would point out that the Yorkist pretentions to the throne didn't begin in 1455, and neither did their antagonism of the Lancastrians. There was a clearly established Yorkist faction before 1455, and intermittent Yorkist faction leaders had made claims to be the superior candidate to the throne since Henry IV had taken England from Richard II. The Lancastrians wouldn't take the Yorkists waltzing into Whitehall lying down. They would find their own candidate from somewhere. Remember how tenuous Henry VII's claim was when he led the Lancastrian party into Bosworth Field.