It won't be anywhere near a billion.
China already has an average of ~1.7 children per family [0] if you factor into account that the policy is enforced at a provincial level, and depending on that province, it may be the case that (0) people of certain backgrounds (e.g. farmers, minorities, parents with disabilities or medical conditions) can be exempt in some areas, (1) affluent people sometimes just pay the fine and have a second child, (2) in the most recent version of the law, if one parent is an only child, they were permitted have 2 children, (3) Chinese citizens who have resided overseas for some period of time may be permitted to have 2 children.
A lot of people may go from 1 to 2 children. Not that many people will go from 2 to 3 children. Children are very expensive for most families.
[0] http://data.worldbank.org/indicator/SP.DYN.TFRT.IN