My work: http://www.fanfiction.net/~outside85
Of course Constantine could be on a team. Not a typical superhero team, sure, but he's got PLENTY of friends, had plenty of relationships throughout his career. One need only look at his first appearance to see him assembling a team of helpful, like minded individuals. Sure they didn't have super powers, but they believed in the occult.
You look at something like Grant Morrison's JLA, and I'd argue that we had some very good character moments, but that it was a plot driven book. I have a feeling we'll be getting something more in line with that.
But Lemire said it best; his ability is one of persuasion. It makes total sense that he'll get people to help him do what needs be done.
And if you'll look at Lemire's plan, it's very much to have all the other characters rotate. Deadman can't die, by definition, and Zatanna has been 'putting up' with Constantine for years now, so it's no surprise that they'll be around.
Everyone else need only tolerate him for an arc or two, from the sounds of things, save for Black Orchid who I suspect is going to be Abbey, and come with her own baggage.