Not really. Centrelink generally goes with whatever you tell them the situation is, unless they do their own audit/investigation.
Secondly, and contrary to popular belief, a person's centrelink "status" rarely directly affects a person's status in other areas of law - for example family law. Same would go for this sort of tenancy matter.
Lastly, it's pretty hard to get information on another person's entitlement anyway.
Whichever you take it and it was meant as wry humour, you might agree that those who habitually do the wrong thing and have scant respect for agreements, can come to a sticky end. But even if they don't, they foolishly complicate their life.
'Generally' is not a robust assurance there will be no check as a routine or as internal QA. The data matching with other agencies is surprising.
It is a fact that a tenant who is prepared to mislead or defraud an owner on occupancy does run the risk of a complaint to Centrelink where the tenant could be receiving Centrelink benefits. Centrelink encourages such reporting, 'dob-ins', saying that it renders a public service. One phone call and it could be 'problem solved' for the owner or PM who doesn't want that unapproved long stayer and the games associated with him/her.
Others can be the judge of that and it is not something I would go out of my way to do, but idiotic tenant misrepresentation/false reporting to owners regarding occupancy could run risks for the tenant. As well, it is reasonable to suspect that any tenant and her/his live-in 'guest' who isn't prepared to live up to his/her side of the contract is also likely to present problems in other ways. Behaviour generalises.
Would you encourage anyone to test Centrelink? It does investigate all complaints and there are penalties.
Apart from that, a tenant who sets out to breach the agreement, even where they are cunning enough to find sly ways to frustrate and exasperate owners and PMs, will eventually find himself being required to find alternative accommodation. Owners and PMs have better things to do than put up with nuisances, who multiply management overheads.