Hi,
Does your roommate's ex (child's mother) still live in the same state as your roommate (child's father)? It does not sound like she is relocating the child.
You mentioned a private custody agreement. Is this court sanctioned? If not, the mother can move the child to another state or country as she pleases. To recover him, the father will need to apply to court for a recovery order. However, given that there does not appear to be a risk of permanent relocation, and the mother seems to be just extending a well-intentioned holiday, the court may refuse to make the order for immediate recovery and adjourn the matter to wait for the mother to return from the holiday herself, with her son.
A Centrelink status is different from a custody status. It's really more for determination of Centrelink payments. It does not allocate custody rights.
This appears to be better resolved in family mediation, rather than court. It seems to be more of a domestic issue (communication, managing expectations, parenting decisions) unless the mother appears to be moving the child interstate permanently.
If this goes to court, the ONLY consideration would be: what is best for your roommate's son? While your roommate may miss his son, as any good father would, he should be asking what is in his son's best interests? Is his son enjoying the vacation? Is there another reason to have his son back, other than your roommate missing him (e.g. missing school, medical care)?