If at some point during the Commonwealth Cromwell had, like Bonaparte 140 or so years later taken the title of Emperor rather than Lord Protector (or in Nappy's case Consul) would it have granted enough legitimacy for his son to follow him? Lord Protector was a title no one knew how to relate to. What were his powers to be, and what checks on those powers, if any to be?
While there would still have been those questions, it was understood by the educated, that an Emperor was more than a King.