Uh, no.
The ratification of the Constitution( of which the 2nd Amendment was a key) was upheld by SCOTUS in the cases I cited.
The US Constitution was ratified on June 21, 1788.
The 2nd Amendment (which was the 4th one put up, not the 2nd) was
proposed on Sept. 25, 1789, along with 11 others. It was not ratified until Dec. 15, 1791, nearly 3 and a half years after the Constitution.
No, the subsequently enumerated 2nd Amendment was
not key to the ratification of the Constitution.