Yes the gas company can still shut your gas service off to your home even if you have children.
Having children doesn't make it so that the gas company or other utilities can't shut you off so you can still be shut off for non payment.
There is an exception though that during the winter months there's usually a law in most states that makes it illegal for you natural gas or other utilities to be shut off during the winter.
The law goes into effect starting November 1st and goes through March 31st.