No it's not. Humans don't have genetic memory. Five and a half centuries won't rewrite history or undo biology.

: Such a grand species going from a Halo to a cave of
: their own accord is something I really doubt would ever happen.

Meanwhile, this is completely within the realm of possibility. The "of their own accord" part is less likely, but it's also not required. Have you ever heard of feral children? What about the dark ages? How about the Middle East, and what they lost after the Mongols steamrolled them?

: Even then, Bungie's intentions with the Human-Forerunner connection seems vague.

That's part of the problem too. They've taken all the mystery out of the Forerunners. Ordinarily I'm all for mysteries being solved and questions being answered, but for this I was fine with just little bits coming through in architecture and machinery and text logs.

: 343 Guilty Spark speaks very strangely. He refers to John like they've met
: ions ago, and despite being almost entirely human, is referred to as a
: Forerunner. It honestly seems like 343i's geas and related structures are
: rooted well in Bungie's mythos for Halo.

343 Guilty Spark is a hundred-thousand-year-old floating computer, honestly it should be more strange he speaks so normally. I've thought since Halo 2 referring to him like they've met was a tie to some fiction point that was later cut. The geas thing is supported in the book based on the first game, but that was written (AFAIK) without input from Bungie, and by a different author from the main line of books at the time who set a lot of the other foundational fiction. As for the rest, I'll point you here.

I also don't think 343i knows what to do with the Forerunner-- they took out the mystery, they put in this whole geas thing that doesn't make sense, they added this soap-opera-style second Didact for no good reason, they resurrected 343 GS, they didn't so much as mention Mendicant Bias in Halo 4 and might be bringing him back in Halo 5, they gave them weak, bland weapons, and they made them call themselves the Forerunners, which sounds like something an 11-year-old would do because they don't understand how translation and cross-cultural naming happen and insists the games call them the Forerunner so that's their actual name. The last one especially worries me because they really might think the players won't get it, because the have untranslated Sangheili referring to the Didact as "Didact" and the Prometheans as "Promethean" in Halo 4.