Could a cardinal or pope have children if they are a widower?

Could it be possible for a cardinal,or even the pope to have children,if he had been married previously,and then taken up holy orders after being widowed? This would seem to fulfil the requirements of not being married and also being celibate whilst being a priest,but I can't find a definitive answer-all the celibacy guidelines seem to just refer to during the period of the priesthood.