It depends on whether the child has Indian citizenship or not.
According to India's Citizenship Act, a child born abroad to at least one Indian citizen parent is an Indian citizen by descent if the child is registered at an Indian consulate within one year of birth, and the parent declares that the child does not hold a foreign passport. The child would have to renounce other nationalities within 6 months of age of majority or lose Indian citizenship.
So if you register the child, and do not get a Canadian passport for the child, the child will have both Canadian and Indian citizenships, at least until 18.5, and in this case, the child can live in India with all the rights of an Indian citizen just like any other Indian citizen. However, it will be problematic for the child to return to Canada after leaving, without losing Indian citizenship, because as a Canadian citizen, the child cannot get a Canadian visa, so the child has no document that will convince an airline to let them board on a flight to Canada, other than a Canadian passport. And getting a Canadian passport will cause the child to lose Indian citizenship.