[Archer leaps into the life of Aussie Prime Minister Bendere Dundat at the launch of the RAAF space shuttle]
“Oh, boy…”
Is it sad to admit that even though I’m a rank TNG amateur, this thread has given me a massive fit of the giggles?
I’m reminded of the episode The High Ground, which raised a similar issue. In a premise (perhaps deliberately) reminiscent of Northern Ireland, the planetary government of Rutia IV had a near-perpetual insurrection by Ansata separatists. The terrorists who kidnapped Crusher claimed that the Federation was effectively causing the government to refuse to even consider Ansatan independence because that would mean Rutia IV would no longer be a united planet and would lose its contacts with the Federation.
“It’s hardly analogous, Beverly, since as you well know the Australian population became extinct in 2156 after Bruce, head of the Woolloomooloo University Department of Physics, blew up the continent with a thermonuclear bomb when he tried to do a practical joke on that pommie poofter professor Bruce of the Philosophy Department.”
Was his name not Michael, then? I can see why that could cause confusion.
I agree that Picard was probably just going to note that Australia was not actively hostile towards the United Earth government. If it opted out, UE could still join/help found the Federation, and Australia would just be a non-Federation enclave, just as it was already a non-UE enclave.
As it happens, this issue has arisen in a ST:TOS-era RPG game I’m now involved in. The current mission is about first contact with a planet that has recently developed warp drive, but is still divided into mutually-antagonistic nation-states, as it strives to become eligible for admission into the Federation.
“Bazinga!” 
Australia itself survived this separatist movement 
Funnily enough the reference to Irish reunification in 2024 was cut from it when it aired on Sky and the BBC refused to air the episode at all until 2007.