I'd say it's relatively easy to incorporate most Wildstorm characters, and even teams like WildCATS or Gen13 into the DCU. Even the predecessor of The Authority, Stormwatch, could easily be revamped as a governmental rival (whether as a UN organisation, or NATO, or even just the US) to the non-governmental Justice League. But the Authority was founded as a non-governmental super-team on a global scale to fill the void when Stormwatch was disbanded.
To have it make sense in a universe where the Justice League also exists, it would have to have different reason to exist. It could borrow that from the original Outsiders team, I suppose, where they are willing to break international law and go after dictators. But even that seems like a stretch in James Gunn's DCU, where Superman and the Justice Gang themselves did that to a degree.
I did think, after Gunn said Hawkgirl killing Ghurkos would have consequences, that this would lead to the Justice Gang adopting an official no-kill rule, and The Authority could be founded as a counterpoint to that. But, apparently, that's not how this is going to go.