Without Cortana left behind to be interrogated and violated by the Gravemind, would her rampancy had been forestalled and could this have possibly had an impact during critical future events?
She wouldn’t have gone Rampant, and the entire universe would have been doomed as the UNSC would have never found out about the Ark and the incomplete Halo Ring. The UNSC would have stayed to fortify Earth after Truth and his fleet left through the Voi Portal, the Gravemind would have most likely infested Earth, and everyone would have died either by becoming Flood, or with Truth being able to activate the Halo Array and wiping out all life in the galaxy (likely permanently, as there was no Conservation Measure in place).
At best, the only immediate net positive of Cortana staying with the Chief at the end of Halo 2 would have been a possibly more successful mission onboard the Forerunner Keyship, possibly allowing him to assassinate Truth. But that wouldn’t have helped, given that Truth is required to get to Earth and excavate the Portal in order for the UNSC to gain access to the Ark, which they wouldn’t know about anyway.
So in that scenario, the Flood shows up and infects everyone, and the entire galaxy is consumed.
Not really to many speculative paths to take on this topic.
I doubt it. Cortana had been in service 8 years by the time she woke Chief up on the FUD. An AI service life is 7 years. She was already well past pushing the limits.
Tin foil hat time
If anything, it lends credence to the theory that the Gravemind actually kept Cortana going so that she could remain unwittingly in service to his plan. She remained alive just long enough to fall into the Domain, be “reborn”, and conquer the galaxy. This has left the galaxy vulnerable and weak. Ripe for a Flood attack. The Gravemind said it was like water. It ebbs and flows, but cannot be completely destroyed. There’s a possibility that the Gravemind is out there waiting to strike. Even if there isn’t enough biomass for the Flood to reconstitute the Gravemind now, if they gather enough, a Gravemind will be formed and it will have all the knowledge of the past Gravemind.
The Precursors are incorporeal and timeless, and the Flood are a tool they use to manipulate galactic events to their desired end.
If Cortana hadn’t been left on High Charity, Humanity would still have learned about the Ark, and the showdown would have still happened on the Halo above the Ark. And Cortana is a UNSC Smart AI, so without the infinite processing power of the Domain, she would still have gone rampant. And I fully expect the Flood would have managed to talk to her somehow, even without her falling into its custody, so she’d still carry the Logic Plague.