Essentially no. The position of pope as we recognise it now didn't really exist, and no emperor ever attempted to claim the position of the time we now call "pope". Those in the time period that we now call "pope" would have been seen at the time as simply the bishop of Rome. While this was certainly one of the more important bishoprics, it was not seen as the undisputed master of Catholicism as it is today - Alexandria and Constantinople were of at least similar influence.

Given that, the emperors had a vast amount of power over the Catholic church, and at points were very involved in major church rulings, for example with Theodosius I and the second ecumenical council. This meant that in a way the emperors were able to act as an ultimate arbiter above all the bishops, like the pope, but were far from the enshrined head of the church. More of a point of interest rather than meaningful, but the Roman emperors were the holders of the title "pontifex maximus" before it was passed to the bishop of Rome.