The answer is NO. Keep these things separate. The child has some right to part of the family income just because of family membership. It is better to give the child some of this in the form of an allowance. On the other hand, the child has a responsibility to share in routine household tasks, and should not expect money as a reward. Helping around the house, children should learn, is part of belonging to a family.
You can help children earn a little extra money at home. If you have special jobs around the house or farm, or in your family business that you would employ someone else to do, hire your child for the job. Keep the relationship business-like and pay the child a fair wage for performing the service.
Often the money children earn gives them a greater sense of freedom and recognition than money that is given to them. Earning money is good as long as the work is not too strenuous and there is still time for the child to study, play and take part in family activities, family chores and school life.

Additional Resources:

http://edis.ifas.ufl.edu/pdffiles/HE/HE16000.pdf