The short answer to this is NO! If you are ordered to pay child support it is irrelevant whether you see your child or not and here is why, each part of an Order is separate and distinct from the other parts. So for example if you have a child support order you also have an order related to possession and access, an order related to who is the primary conservator and an order related to the rights and duties of each parent. There may be other orders of the court in your specific Order but the above will be included in any original child support order. Each of these parts of the Order are separately enforced and/or modified in later actions. If, for example, you are not able to see your child then you could file an enforcement action against the other parent for not allowing you to see your child. This is not dependent on whether you paid child support. So even if you have not paid the court ordered child support you still have the right to see your child. The other parent could file an enforcement action against you for failing to pay child support, but that parent still HAS to allow you to see your child per the Order.
If you are not being allowed to see your child pursuant to a court order, the proper remedy is an enforcement action against the other parent that is denying the visitation. Enforcement actions require very specific details in order to be granted by the Court, and therefore, it is recommended that you seek an attorney to assist you in filing an enforcement action.