First off, the early christian church was actually quite open about its practices to members of the church. Sure, to the Romans they appeared secretive because they didn't meet in public, but there was no real clergy until the 3rd century, and even then it was rudimentary. Early on, people could even claim to be prophets of God and offer prophecies for their church (on harvests, etc...) and it was accepted, while later that became considered blasphemy. Furthermore, the practices for Christians were fairly simple. Something called the Agape feast, which is basically an early Eucharist, was practiced regularly, but besides that there was very little uniformity amongst churches. The attempt to define orthodoxy didn't really arise until the 3rd century as well.

Ok. On to the question. In my opinion, the answer is no. Just as the early Christian church had no set theology, or christological stance, the pagan religions (as in the Imperial Cult and the traditional belief in the Roman gods) did not have dogma, so much as they did have correct methods of practice. It was important to know how to pray and sacrifice, but not so much to consider the origins and meanings of the gods. There was also an expectation to sacrifice, especially for the imperial cult, and there were religious festivals, but really the only thing kept from the layman worshipper was access to the interior of temples, where relics and images of particular gods were stored.

There are, of course, the mystery religions of Rome as well, that did become quite popular. Some were fairly open, but others, such as Mithraism, remained secretive. Those wishing to join the cult of Mithras had to undergo several stages of initiation before entering the cult, similar to catechetical teachings before baptism in the early Christian church.