Legally, no. He is subjecting himself to contempt of Court which may carry jail time and a $500.00 fine. Visitation and Child Support are two separate obligations. It doesn't matter if you owe $1,000.000.00 in back child support, the other party cannot withhold the children. Likewise, it doesn't matter if the other party never sees the children at all, (and that's fine with you), she still has to pay the child support.
In some instances, I can handle these types of cases for a nominal fee. It depends on the facts of the case.