No and No.

Historical English "Commons" had a set of unwritten rules describing exactly who could do what when. Generally each family from the local village could cut so much wood, hunt this or that at such and such a time, graze a certain amount of animals in a certain season, etc. It was hashed out informally in villages and enforced by a combination of local courts, peer pressure, ostracism and running off strangers from outside the village. There is not much evidence that common land became overused in historical fact.

The Enclosure act did increase grain production in England. England would have been a net importer of grain otherwise. The Napoleonic wars interrupting grain imports, and later the "corn laws" (tariffs), made turning commons into ploughland profitable for a few decades. Britain Being self-sufficient in grain was a perceived benefit to the upper classes. Perhaps cheaper food prices for the urban population smoothed the course of the industrial revolution. Mostly though, enclosures were a way for monied interests to better exploit the countryside.

None of this means that the "Tragedy of the Commons" as an economic or game theory principle can't happen, it just means that the historical example used to coin the phrase wasn't apt. Perhaps it could be said that low transaction costs (locals who know each other and can easily communicate) in the historical example illustrate how a commons problem can be solved.