Not in Jack Kirby's original vision for the New Gods in it the plan was never to get the New Gods to join the main DC Universe. But things change and they merged it. But it led to Darkseid butting heads with Superman more times than the people of New Genesis or even Orion his son that he gave away as part of a treaty with New Genesis. It makes better sense for Darkseid to butt heads with New Genesis and the Green lantern Corp than for him to lock horns with Superman. That's true but there's no rule saying it has to be Hal, Kyle, John, or Guy to headline your Green Lantern mystery series so you're at perfect liberty do it. Or as I brought it up before Englentine's idea to put Simon and Jessica under Kilowog's command.