This would include her American descendants by Sir Eustace Hart ( "joke name" for King James I).The descendants of Mary de Vere were eventually the closest by blood to Edward de Vere, 17th Earl of Oxford, Lord Great Chamberlain
Charles N. Pope believes that the John Hart who eventually came to America was John Casimir (Hart), King of Poland and one time Jesuit Cardinal. https://en.wikipedia.org/wiki/John_II_Casimir_VasaExcept for public family trees, the documentation and very existence of John Hart appeared to have been "scrubbed" (as Miles Mathis might put it), so that no one could make an American connection from Declaration of Independence Signer John Hart back to Edward de Vere and Francis Bacon.
According to his Wikipedia biography, Yes: "On 16 September 1668, grief-stricken after the death of his wife in the previous year, John II Casimir abdicated the throne of the Polish-Lithuanian Commonwealth and returned to France, where he rejoined the Jesuits and became abbot of Abbey of Saint-Germain-des-Prés in Paris."Or, is it once a Jesuit always a Jesuit?
The following examples will show you how Byzantine the relationships can be from this family (after all, they were once Byzantine Emperors themselves). After the Civil War, a descendant of this Vere/Hart American family married the great-great-grandaunt of the heir to the third largest cranberry producer in the United States, who also became a Republican county chairman and "boss", whom a former governor called "the chairman of the chairmen". This "boss" was the first cousin of the father of Kellyanne Conway, former counselor to the President. In turn, Kellyanne Conway is the first cousin of the father of Giovanna Coia, a White House press assistant, who last year married John Pence, the nephew of VP Mike Pence, and who is a senior advisor for the Trump campaign.officially unrecorded son John Hart, presumed to be the founder of the Vere/Hart American family.