I take it from the covers and solicitations that they aren't doing this, but it'd be neat if the Justice League refused to give Superdad Superman's spot. Think of it from their perspective: Why should they? They have every reason to be suspicious of this alternate reality Superman who's 20 years older than their guy. They may meet him in the final month or so of their Superman's life, and he may help them or seem like a good guy, but they don't really know him. They've met at least one evil Superman alternate from another universe. Would you just hand him the keys to the Justice League satellite and all that advanced tech and knowledge about the world's heroes that he could use against you?
Usually, they kind of do a vetting before letting a new superhero join the team. Remember, how Green Arrow wanted in and they said no? From the Justice League's perspective, why would you treat this alternate Superman any differently from any new superhero type to appear on the scene? I mean, you might want to get to know him or not want to get to know him because he's an alternate of your old friend/lover/co-worker, but just being his duplicate from an alternate dimension doesn't mean he's good or trustworthy. You'd think think they'd hesitate. If Lex Luthor is still a member of the League, you'd *really* think they'd hesitate (I can't imagine him being easy on any version of Superman). Of course, Lex isn't in the promotional images of the Rebirth Justice League, so maybe he's just going Metropolis only with the Darkseid War ending.
I mean, to me, realistically, the only two people I could see just going along with this copy and paste Superman, if they write this like it'd really happen, would be the two Green Lantern rookies, who'd be the low people on the totem poll and not really be in position to complain about decisions made by the more established remaining members, and who wouldn't necessarily see Superdad as a weird duplicate trying to replace their friend. Jessica only knew Superman a little bit, and the new male Green Lantern not at all.