Depends what your paperwork says but if he is behind on child support, he will not be able to claim unless the paperwork says he does get to even if he is behind on child support. Call your local child support office and ask them, they usually have access to your file and can tell you.
Do you have an employee handbook or employment contract? Review it and see if it requires notification. Usually if there is such a provision, it is for criminal convictions which an OWI 1st is not, it is civil (it is a ticket)