Yes, even a crudely formulated childish prayer has in it a real power. This power of the prayer lies in the bhaava, the inner state from which it emerges. Its significance lies in the fact that it brings us in contact with the Divine. It is like reaching the river or the sea. Whether a person came with dirt upon his body or all neat and clean, the river still would cleanse. So too even a crudely formulated prayer can bring us in contact with the Divine which will eventually have a cleansing effect upon us.
Follow up of previous question