While many Christians were killed by Nero's persecution, many people in the society who watched the Christians' death in the Colosseum and witnessed their persecution began to sympathize with Christianity. This led to some of these people converting to Christianity. The persecution of Christians seemed to actually encourage the growth of Christianity, until under Constantine when Christianity was made the religion of the empire. Tertullian (early church father) wrote "the blood of the martyrs is the seed of the church", what he meant by this is that the more that Christians were persecuted the more the number of converts grew.
While we do not have completely accurate information on religious populations in Ancient Rome, it is generally believed that the number of Christians in Rome increased even as Nero was persecuting them. The reason that is typically given for this is that the message of Christianity was so compelling that many people chose to follow the new faith.
Scholars typically say that the Christian message appealed strongly to many people in Rome. For example, it was welcomed by the poor and by women. These groups welcomed the ideas of Christianity because Christianity preached the inherent equality and importance of all people. This meant that even the poor could feel that they were important in the Christian faith.
Scholars also point out that Christianity spread because of the missionary efforts of its members. Christians were very interested in converting people to their faith. It was relatively easy for them to do so because travel around the Roman Empire was fairly easy.
Scholars argue, then, that the Christian population of Rome increased even under persecution because of the work of the missionaries and because the faith that they preached was so appealing to many Romans.