No, it doesn't actually have any effect on tax laws. The IRS has their own rules and generally for their purposes a court order won't sway a decision about claiming a child. However, and this isn't insignificant, if someone is under court order to allow another party to claim the child and doesn't do so then that person is in contempt of court. Judges generally don't like it when individuals fail to follow their orders, so while the sanction for this varies widely - it is far from no big deal.
In practical terms what this means is that if the wrong party claims a dependent, the place to take that up is in the court where the order was issued and not at the IRS.
