Yes - I encourage everyone to go through Domestic Relations when you set up CS...even if you do not use your state's required CS payments (ie you guys agreed on your own amount).
If you ever run into a problem, it is a lot easier for the state to help if it is processed and transactions recorded through their system.
My neighbor just got a 'government intercepted' check for back CS. Her son is an adult and long gone (on his own) but they said it doesn't matter, his dad still owes that money.
He keeps working under the table to avoid garnishing but she said once he files for Social Security, it will be garnished?
She said it will be 30 years late by then....but she will wait for it