The One Child Policy had some effect but not as much as thought.
Fertility had already decreased significantly before the policy was introduced. I also know Chinese demographers who think the current fertility rate of China is underestimated due to the under-reporting of births.
If you look at Taiwan, made up nearly entirely of Han Chinese, where people have as many children as they wish, it has the lowest fertility in the world - one child per woman!
Chinese in Hong Kong, Macao and Singapore all have 'lowest-low' fertility well below 1.5 children per woman.
I also don't think that China will be too successful in increasing fertility now. What they need to do is reform their public pensions and face up to the fact that an ageing population is going to happen.