One must be careful about taking analogies beyond their intended scope. A few facts relative to the question to help set the background here include:
- Amniotic fluid, though it starts pure, later can include the fetal excrement (called meconium).
- Noah's family spent far more than 40 days in the ark. The rains fell for 40 days, but they were in the ark from seven days prior until the floodwaters abated and the land was dried enough for Noah to come out about a year afterward.
- Noah and his family were already counted righteous before the Flood.
It was the entire earth whose sins (sinners) were washed clean during the Flood. Baptism is a symbol of cleansing from sin. So, rather than Noah having been baptized, one might actually consider the earth as having been baptized.
There is a connection, however, to the water of birth. There is a legitimate parallel to be made between physical birth and spiritual birth. The connection is that of a beginning. Each birth begins a new life: one, a physical life, and one, a spiritual life. And each life begins in assumed innocence.
From my perspective, I would see it almost the other way around from the perspective of the question. I would see physical birth as a symbol of the spiritual new birth that is of utmost importance to God. No one remembers being born physically, but we are able to look back on that day vicariously and draw lessons from it for our spiritual life.