Yes, it is possible. This is because unemployment benefits are measured income for the functions of child support, just like they are measured to be income for purposes of federal income taxes. You should first consult your nearest department of child support services to find out more details.
Most states do a check for legal obligations like child support when any state-funded payment program is involved. Many states have laws that require that these kinds of payments be debited for outstanding obligations like child support (and in some cases other things like victims compensation awards) to ensure that they are paid.