Forgive me if i'm out of line for saying this, as i'm fairly new around here, but I think that we should keep this on topic, this is "Colossus what if?", not "Knossos what if?". 
yer but that discussion hit a fairly natural end and it evolved into a wider discussion on the survival of the GTVA against future shivan encounters which is on a tangent but related to the original discussion, it happens a lot around here and so long as it's all related, sensible and kept clean its all good.
If you have a point to make on the original theme then you are free to reference the stage of the discussion you need and make your point.
Firstly assumption you make there is that Shivan forces are on top of the node on reactivation which is not forced to be the case. Also we don't know how much time passed between the Trinity activating the knossos and the Rakshasa entering GD and killing the Vigilant.
Since we're talking about the universal destroyers with an almost-unstoppable fleet, I'd rather not tempt luck.
while it's true that the Shivans have access to a massive fleet and you or I would steam roll the GTVA, we have to look at how the shivans act in game and they rarely do this and what we tend to see is smaller combat actions leading up to the big hammer blow. It could be that over the millennia the shivans have been back footed often enough to settle on a cautious strategy because some times these insignificant whelps do something brilliant and it cost them dearly.
Secondly evidence from the destruction of the Vigilant and the events in GD is that the Shivans send a small recon force through first, cruisers and fighters, and deploy the big stuff later on.
Same answer as above.
ditto
Typically i'll try to avoid posting around this time (because my posts' quality is close to spam when i'm tired), but I do believe a command briefing in the FS2 main campaign mentions the Knossos being something along the lines of inactive before the Trinity unleashed some really angry Shivans.
Anyway...
Forgive me if i'm out of line for saying this, as i'm fairly new around here, but I think that we should keep this on topic, this is "Colossus what if?", not "Knossos what if?". 
Which only proves the Knossos can reopen closed nodes. It doesn't necessarily proves it can close nodes that are already open (and if it can, why didn't the Alliance just closed the first Knossos instead of destroying it?)
Research into the Knossos was incomplete and the possible systems involved in a shut down were not tested due to alliance orders that the portal remained open for study
Back on topic, I'll risk the conclusion that, since we don't know what the GTVA would have become anyway, the answer to the original question is simply "we can't know".
If I have to speculate, it would have been left active for a few months, just in case the Shivans decided to show up again. Then it would have been decommissioned and put in reserve, since there's no sense in keeping that resource-devouring monstrosity in active service when there are no wars.
The GTVA would have bounced along for a little while at least, I think the most likely GTVA fall scenario would be that the vasudans withdraw from the alliance leaving the Terrans to bicker and fall apart aka post FS1 era/early reconstruction era. after some time the terrans would probably start getting their act together and refornm a central terran power block and probably start negotiating a resurrected GTVA in some form