From the looks of it, they won't actually be.
Let me explain. In Old Man Logan, the character is made to visit several domains (in this issue, Armor Wars' Technopolis, for example), cutting him off from his home domain, a postapocalyptic future similar to the original Old Man Logan's. While some characters in Secret Wars know all about other domains and do move about, most do not. Old Man Logan is certainly bewildered by his meeting people he knows, but who don't know him. It appears his domain really IS the future of Earth-616 (or at least has a past that is exactly like 616's), so if he were to move to a reconstructed universe, as it were, he would "know it" as his past. As someone who "remembers" the former universe (in a way), he's primed to move back there with a minimum of fuss. He might even be one of the few people who remembers Battleworld when all's been said and done. But that doesn't make him a "continuity implant" retroactively inserted into the Marvel time line; it gives him the status of refugee. From Battleworld, from an alternate future, call it what you will. Is that what's ahead for the Squadron Supreme and the Ultimates? Will they remember their former worlds and have to adapt to the new one? Looks like it. We won't be looking at a Marvel Universe where the Squadron was operating in upstate New York, somehow, or has been born anew.
My guess is that certain characters will join the fight near the end of the event and get a chance to escape Battleworld's destruction, finding their way to the new Earth, much as the twin ships of Reed Richards and Thanos did, from the colliding universes to Battleworld. Speaking of which, the one new series out this week is Star-Lord and Kitty Pryde, and it's the first outside the core book to feature a character from the previous universe. This is the Peter Quill from our world, and he's just laying low after being scattered to the winds by Dr. Strange (at least until he meets a Battleworld Kitty who works for Doom). It's not necessarily part of the larger core story, however, just a side-trip for one of the refugees, though it does reference it and the location from Attilan Rising. If you're not reading the whole thing, this stands as a warning.
Now then, here are my picks for 5 Favorite Moments of the Week (spoilers ahead)...
5. Even though it's Ragnarok out there, it's not too late to put someone in their place.