Will a nursing baby have added DNA transfer from the mother by ingesting cells that might be present in the breast milk, and does this have karmic consequences of significance?

There is a minor transfer that can happen but this is only a very minor influence compared to the proximity of the infant with the mother and the deep bonds created through interacting physically, and emotionally, and mentally all during life, particularly the early years, so any such transfer of a second-hand link to the mother will be very minor in significance.