Hardly. Russia invading the Ukraine is clearly rather different to a Argentina invading some rocks 8,000 miles away from the UK. If Argentina had annexed the Isle of White and then started a civil war in Devon and Cornwall the situations might be a bit more comparable don't you think?
The comparison is that part of the UK was invaded, and the country doing the invasion either didn't consider the fact that we had nuclear weapons, or calculated (presumably, correctly) that they were irrelevant because there was no way we'd have used them. And in my view that rather illustrates a problem: What do nuclear weapons deter against? Since the consequence of using them would be horrific, the provocation that might cause a country to use them would have to be extraordinary. You suggest Argentina annexing the Isle of Wight. I rather doubt that even something like that would be considered justification for - in effect - murdering hundreds of thousands of innocent civilians who happen to be Argentinian, so I rather suspect that even in that situation, use of nuclear weapons would have been out of the question, and our nuclear capability would therefore not have posed a deterrent.
So that raises the question: What possible plausible threat could nuclear weapons deter against? Maybe someone trying to exterminate a substantial portion of the UK population would be the kind of thing that might legitimately provoke a nuclear response, but the groups likely to want to do that are terrorist groups, who, as you imply, are not likely to be put off by nuclear weapons. The only vaguely plausible possibility I can think is a rogue Government like North Korea.
Of course if there was no cost to having nuclear weapons then you could put a good case for having them on a 'just in case' basis. But the cost of replacing Trident is huge - and I imagine would be enough to pay for - for example - a pretty substantial boost to our conventional forces, which seems rather more likely to be actually used (for example, that is what ultimately freed the Falkland Islands).
On balance I'm undecided on the issues, I can see arguments on both sides. But I don't think that picking on current conflicts (such as Ukraine) and saying, if they'd had nuclear weapons..., when it's patently obvious that it would have been politically impossible to use them anyway, because that would have amounted to such an overreaction, makes for a good argument.