So as we all know, when this show was announced they made it pretty clear that it wasn't going to be connected to the Arrowverse. But they said the same thing about Supergirl, and look where we are now. The move to the CW only makes it that much more likely in my opinion. There's no reason to have the show on the same channel with some of the same producers and not at least do some crossovers, even if the show occupies its own Earth within the Arrowverse as Supergirl, Freedom Fighters: the Ray, and The Flash (1990) do. I think this would be a nice chance to flesh out Supergirl's Earth. I'd love to see Black Lightning officially take place on Earth-38. With Flash, Arrow, Legends, Vixen, and Constantine all taking place on Earth-1, it sort of leaves Supergirl on an island.