Did the Puritan belief in predestination influence social development in New England colonies before 1670?
You can certainly argue that it did. You can argue that the belief in predestination led to the development of the "Protestant work ethic" that is said to have typified New England.
The Puritans believed in predestination, of course, but they also believed that a person's life could be an indicator of whether he or she was predestined to go to Heaven. Working hard could not get you to Heaven, but it might show that you were headed there. Therefore, Puritans tended to work hard and act soberly so that they could be more confident that they were saved.
In this way, the doctrine of predestination helped to make New England develop into a society of hard-working and relatively straight-laced people.