The fact that throughout the Apostolic Age and into the early Church there were persecutions by Roman and Jewish authorities in no way counters argument of influence.  Unfortunately, triumphalism is not countered by the argument of the crucifixion of Jesus or the deaths of the Apostles but can find its support in the fact that Christianity survived and thrived after such.  This is not an argument in support of triumphalism, however, but evidence of the Triumph of Christ.
Yes, all had influence, which survives both in Scripture and in the body of the Church.