Yes, because they were all classified as being the children of unwed mothers. The government could not claim that he was responsible for providing for them, any more than they would if it were any child support case. Thus, they look at the income of the mother, and the child support the father can provide, and determine that it is not enough.
However, if they are legally married, then the mother and father are considered as a married couple, and they are evaluated as a married couple. As I said, there has to be regulation of the eligible dependents, but the state would no longer consider each wife to be a separate entity requiring single mother welfare support, and therefore the welfare payout wouldn't be a means to prosper, any more than any other married couple on welfare.