"For Christ did not send me to baptize, but to preach the gospel - not with words of human wisdom, lest the cross of Christ be emptied of its power." (1 Corinthians 1:17) How can a C-of-C'er read this and not freak out? If I believed the act of immersion was required to be saved, then I would be confused or livid after reading this. Why would Paul give people only half of what they needed? That'd be like feeding people D-amino acids and watching them starve while thinking they were being nourished!
I think this verse reminds me of 1 Corinthians 3:6: "I planted the seed, Apollos watered it, but God made it grow." There's stages in the Christian life. Before the seed of the Gospel can be planted in a person's heart, their "heart-soil" must be prepared. For some this is easier than others, because of differences in familiarity with Scripture, openness to talking about spiritual things, and the state of their will. When all is ready, and that person chooses Christ, the seed is planted. Since they've chosen Christ, are they saved? Yes! Is this all there is to the Christian life? No! There's so much more to learn and do. As James 1:4 says, "Perseverance must finish its work so that you may be mature and complete, not lacking anything." One of the first acts of obedience is baptism. But this act of obedience happens after a person surrenders their life to Christ the first time.
So, Paul came through with the seeds, and some of the people he taught chose to accept the seed of the Gospel. He was out spreading the word as fast as he could: he was a spiritual Johnny Appleseed. He did some cultivating, through his letters and visits, but there were others like Timothy who were the heavy duty cultivators. It's a pretty neat picture. One person didn't have to try to be Johnny with the seeds, Johnny with the watering can, Johnny with the hothouse, and Johnny with the pruning shears. It's a body of Christ thing.