How much did voluntary martyrdom by some Christians play a part in the continuation of the Christian persecutions?

From general reading I got the impression Christians were attacked and persecuted when pagans actually reported them to the authorities, because of their different beliefs and unwillingness to participate in the accepted norms and practices of the populace. However, in a piece by G.E.M. de ste. Croix, ‘Why were the early Christians persecuted’ in Past and Present (1963), an interesting point is raised that Christians actually voluntarily admitted to being a Christian in order to be punished and become a martyr.