Hoover would have loved that kind of leverage, methinks.
One little tidbit worth mentioning is that Hoover and LBJ were good friends who had worked together when LBJ was in Congress.
Meanwhile Hoover and the Kennedys hated each other.
I am not sure of Hoover’s role before the fact but I am confident he would have been happy to cooperate with anything the coup plotters wanted or needed as well as playing a key part in the coverup after the fact.