FF #560:
Unsurprising: [spoiler]Mrs. Deneuve is Sue from the future.[/spoiler]
More surprising: [spoiler]Not just a few decades in the future, but 500 YEARS.[/spoiler]
More surprising still: [spoiler]she doesn't appear to be one of the good guys.[/spoiler]
While things don't overlap 100%, I think it's still fair to assume the dystopian future we're seeing here is part of the same timeline as the one in Old Man Logan. If we assume that to be true, that means there's an environmental collapse AND a supervillain takeover, not necessarily in that order.
Are they connected? Well, one hypothesis is that Reed's the Big Bad in Old Man Logan.
Case for: in Civil War, Millar wrote Reed as an amoral character who believed the ends justified the means, and had no problem throwing his friends into the Negative Zone "for the greater good". Faced with the end of the world, this version of Reed could do some pretty nasty things.
Case against: But teaming up with Doom and Magneto to subjugate the human race is a bit of a stretch (no pun intended). Millar also gave Johnny a pretty flexible set of morals for a few issues in there, but once the chips were down he didn't even hesitate to do the right thing. Indeed, Reed's seeming much warmer and more grounded now than he did during CW.
Plus, while OML has thus far focused on a more diverse cast of Marvel characters like Hawkeye, descendants of Hulk and Spider-Man, and a namesake of Kingpin, I think the big bad has to be an X-Man.
Anyhow. I'm guessing "probably not" on the Reed is the President angle -- though he probably has something to do with the heroes disappearing. And I DO think the two catastrophes are going to turn out to be connected, but only tangentially -- Millar's stressed that, while these books tie together, it's not a crossover and they stand alone.
Speaking of, 1985 #5 gives the clearest tie to Millar's other books yet: [spoiler]it ends with a Big Reveal of Galactus, just like FF #559.[/spoiler] Aside from that, transplanting the hero into the Marvel Universe changes the dynamic in entertaining ways -- New Yorkers totally unfazed by two-bit costumed villains in their midst, the Avengers' and Fantastic Four's respective reactions to his request for help, and...well, the solution's obvious. There's one hero in the Marvel Universe who you'd go to if you wanted your crazy story to be taken seriously.
I've said before that man-on-the-street stories are my favorites, and this is a good one. It also manages the proper symmetry for this kind of story. (I remember being disappointed at a Masters of the Universe comic arc a few years back that featured Man-at-Arms trading places with an evil version of himself from an opposite universe; we saw the evil one running around Eternia, but never the far-more-compelling story of Duncan in the other universe. Hell, you go back to Captain N and there was a Mirror World episode, and I remember being irritated that they never tried to team up with the good version of Mother Brain.)