Well, again, this is one of those 'yes they
could, but would they?' questions.
I don't know much (anything?) about FOBS other than what is
here and
here. Neither of those sources say much about how many warheads were carried nor how many FOBS systems were available. IMHO this sounds pretty 'cutting edge'. The Wiki site seems to indicate that it was designed to counter the US early warning systems by attacking from the south pole, and yes, that puts NZ in it's flight path (well, everywhere on the planet was on its flight path) but the point being that if it was used, it was designed to be a sneaky way of attacking the USA. If you've got that kind of asset you're not going to use it to attack a country which (let's face it) is zero threat to the USSR what-so-ever.
Now, I want to be clear here. I have the utmost respect for the NZ military. I've served with some who were in their army and they are good soldiers (and I'm sure the other services are just as good too) but they are just totally unthreatening to the USSR.
Consider this - the USSR and the USA destroy each other with MAD. We end up in some kind of post-nuclear war world where NZ it totally untouched except for fallout (oh joy) and the potential (seems to be less believed these days) of nuclear winter (oh, even more joy). In this TL is NZ really going to use their military to invade the USSR? Is there a higher risk that the nukes used to eliminate this 'threat' are better used on higher threats in Europe, North America, and Asia?
So, I'm pretty sure that they aren't going to use them as a primary strike against a hostile military... and this would be mostly true of the Australian military as well (which, btw is 6.5 times the size of the NZ Military). What other reason have the USSR to attack NZ as opposed to deploying assets to take out a similar threat as Norfolk Island or Madagascar?
Well, they do have a few ELINT facilities that are a part of
AUSCANNZUKUS. This could be hit, true, but most likely it would be more efficient to take it out of action through an EMP weapon, and I'm pretty sure there would be plenty of EMP going on. So really (and this is of course only my opinion) the only threat to the USSR war effort would be that facility which may be a target.
My reasons for thinking it may not be is that it's a part of an overall network. That network would be hit very hard, but not all sites need to be totally obliterated to stop the network from working (although they might for redundancy reasons).
IF FOBS had any left over warheads (and as I said I have no information) then yes it's a possibility. Bombers are another possibility. ICBM's a remote possibility and I'd say SLBM's remote to nil.