Registering a child support/custody order that was obtained in another state or even in another country is accomplished in Massachusetts by following the procedure outlined in M.G.L. c. 209D.
The unequivocal answer is "no." Under Massachusetts law, child support and parenting time are separate matters and a parent's failure to pay child support is not a legal justification to deny or suspend visitation.
Raising a child in Massachusetts is expensive. Both parents share a duty to financially provide for their child, regardless of custody or parental rights. Likewise, every child has a right to financial support from his or her parents. While the court will consider many factors when making a decision on custody, income alone won't prevent a parent from getting custody of his or her child.
In August 2016, President Obama signed the instrument of ratification for the Hague Convention on International Recovery of Child Support and Other Forms of Family Maintenance.