From the gameplay itself, it's suggested to me at least that destroying the nodes has no noticeable affect whatsoever. But that idea goes against the very concept of what a game like this is about.
So I don't think its true.
On the contrary, the whole narrative shouts at you in capital letters how ****ing irrelevant not only your actions really were to the actual course of the war, the entire GTVA actions were also pretty much unable to deviate anything from its own course. The point of having those nodes at that moment was entirely plot-driven. The idea is to have you be inside an alien fighter, inside alien space. You are in a binary system which gives one of your wingmen "the creeps", and you find strange, alien, weird looking shivan node "things" that have lots of powa inside of them. The fact you don't ever get to know about them later is just to reinforce how out of your league you really are, how unknown, and plotwise, unknowable, the shivans truly are (you as the pilot will never understand what those things were in your lifetime).
I'm not addressing the "actual course of the war".
FS2 is very much a story about small victories in the context of a larger defeat. Saving a ship is having consequence. Destroying the capella node is having consequence. Even destroying the initial Sathanas is a victory because if nothing else, it buys time for the GTVA and also gives it the opportunity to gain greater knowledge of the scope of the Shivan threat. Finding the second knossos, an act only made possible by the destruction of the first ship, enables intelligence to go into shivan space. Something that has never been done before.
If the Sathanas was not neutralized, would the Psamtik still be hunting Bosch?
The "hive mind theory" is a simplistic phrase that may well fail to capture every single shivan behavior. What is important to retain is how different in their volition they are to us humans. We care about our singular lives. The shivans don't. They don't care one yota. They will send multiple fighters and corvettes to blow fleeing human ships in Capella even though they "know" they will be wiped out in a matter of moments.
When the Vasudans rammed their Anubis fighters into GTA ships did they care about their lives? When the Colossus stood its ground against suicidal odds, or the NTF did its best to destroy it, did they demonstrate a concern for their own lives?
There's a difference between not caring about survival, and caring about an ideal so much that survival instinct is over-ridden.
The Shivans demonstrate a singular conviction towards their goals. This doesn't prove they don't care about existence.
This is a hint that their actions are not of singular conscious beings. The evidence from FS1 about how their fleet loses efficiency after the Lucifer is wiped out is further proof that there's something along the lines of "hive mind" in motion, which could be taken in multiple ways.
That depends on the specific effects.
If the lack of potency in the shivans was strategic ineptitude, but they were still potent on a tactical level, that could be just as easily explainable as a loss of command structure.
If the fighters rather aimed worse, manoeuvred worse and perhaps were even less efficient internally that suggest a constant connection to a central mind. But a constant connection and a lack of awareness in the spy missions don't work together in my opinion.
The very concept of a hive mind to my understanding is that it is unstructured.
We could imagine them to be absolutely hierarchical with one ship commanding everything else. This is clearly not the case, "lose efficicency", not become dead. But they could well share intelligence and "consciousness" (or not). They could be aware of their own ships not being "their own" or not. Just because the shivans are able to see other shivan fighters and not immediately assume they are not theirs is not a shut case against the hive theory. We can postulate that, for instance, this notion is not automatic, they were distracted and just assumed they were looking "at themselves" and dwelled no further into such thoughts, etc.
The idea of distraction is a bit silly when you consider the tasks assigned to the fighter craft and the strategic importance of the target being evaluated. When the Lucifer entered in-system, would it not be immediately aware of what assets were at its disposal and would it then not re-deploy them to best effect? And when one fighter failed to comply with the will of the whole, would not that fighter be immediately subjected to more intense evaluation? Particularly by a set of craft whose purpose is to evaluate potential threats to the most important asset in the fleet? Doesn't make a lick of sense. Especially when you consider that in similar circumstances, the GTVA would be more effective in evaluating an enemy threat. If the Colossus jumped into a new system and a fighter wing that wasn't supposed to be there, was there, it would be challenged for ID and mission, etcetera.
I think the more likely answer is that the shivans have a shared purpose either through programming or doctrine enforced over eons of related activity. They're a hive mind in the sense that they have a common goal or purpose, one which overrides all other natural urges, but they're not don't have shared consciousness and they don't lack a central command authority. I think their underlying mission is largely hard-coded, changeable only from a central source and perhaps passed on to them by a local authority like the Lucifer. The lucifer fleet had a specific purpose, the Sathanas had a completely different purpose. Derived of that purpose they lie largely dormant or in holding/roaming states until circumstances evolve to reinitialize their behaviour. But Shivans still get orders passed down a chain of command which they carry out until completed or given new orders.
In FS1 for example, if the shivan fleet's underlying purpose was to assist and guard the Lucifer in its mission to eradicate planetary sentience, then the loss of the Lucifer would not only leave them leaderless but also bereft of their primary goal. Without that they would fall back to secondary objectives of engaging spaceborne targets but without the co-ordination of an all encompassing commander. It would presumably be even worse if they likewise lost all Demon destroyers. The more heads you cut off, the more each body part moves independently.
This would better explain Playing Judas. The Lucifer upon entering in system would not seek out a shared consciousness with what was available, but would rather trust that your Dragon fighter is in-system on a mission given by another shivan asset, which at some point received an order from the Lucifer. Or in other words, the Lucifer assumed it indirectly ordered the fighter to be there. The protecting fighters likewise were given direct orders from the Lucifer to protect it against hostile targets, they only registered the player as a hostile target a certain proximity rather then knowing instinctively that the enemy fighter was not one of them. It also fits with the idea of the shivans as living machines.