A question with preamble...
The first Christians, most were jews, no doubt held to the "laws of Judaism", and viewed their faith in Christ as the natural next step. So even after baptism, they would have kept up with their purification. So we really are talking two different things. Judaism to my Jewish friends the Mikveh is not so much for the cleansing of sin, but a symbolic removal of physical uncleanliness. For example if he touched a dead body, you had to be purified, if you were a dead body you had to be purified before burial, if you ate pork etc. etc..
When I was in college I asked an orthodox Rabbi "what if his daughter kissed a Gentile?" He assured me that the Mikvah would not remove the boot mark from her backside, God would do that in his own time, as he would with the one I would also receive if I got any ideas!
So I guess the Mikvah is similar to baptism in that It is still God who does the Cleansing, but unlike the Mikvah which is purely symbolic, Baptism only works with water and the word.

The early Christians that still practiced Circumcision; would they have baptized at the same time? Would It have been done around the same time? Are there any early Christian writings or scraps thereof that give us detailed accounts of the practices of these early Judeo-Christians? I asked the same question of the Rabbi; what I got was why should he care, he has a hard enough time keeping the law without worrying about the sins of others.
Mark