Rereading the letters, I don't know if it's clear that 343 went back to this for inspiration for Cortana. They may have; it's plausible. However, I do think 343 is going through and making Cortana very similar to a rampant AI from the Marathon universe.

In Cortana's curing of rampancy in Halo 5, she is exhibiting similar behaviour to rampant AIs from Marathon, albeit for ostensibly less selfish reasons.

I like this story. I like Halo 4 going into Halo 5 this way. When Halo 4 came out. I didn't think it was any good. I didn't think what 343 was doing with the story was real Halo. I thought they were trying too hard. However, when I shut off Halo 1-3 in my head, and look at Halo 4 and Halo 5 as fan fiction, or as reboots (that are sequels, somehow), then I can see the new Halo story is quite good. It's very deep. Halo 5's story was classic Bungie. If Bungie had made this game, changed the character names, and called it Marathon 4, then I think everyone would have praised it as a fantastic continuation of the series.

You noticing these parallels in the Cortana Letters is great. While, again, I don't know if 343 made the story after consulting these emails, I definitely think it shows that Halo 5 is continuing Bungie's story traditions in the game.

I seem to remember these being commented upon as non-canon in the past, along with the Halo transmissions, but who knows what 343 will do with it? :)