What? No. They only know the amount you asked them to withhold, and that could get you in trouble if you specify dependents then tell everyone you don't have any or something. Also if someone is living in your house, making less than 4700 for the entire year, they can be claimed as a dependent, which means you don't even have to have kids. How would your work even know?
Most of that stuff is pretty optional, and that's for automatic withholding info. You can correct this all on your tax return. This form is more for you to have convenience during return time, and it even says you can exempt yourself from the form for multiple conditions. I don't see why you need to get paid in cash still, like your original comment.