Wouldn't be sure about that. Same as it wouldn't surprise me, if Eden joins Green Day for longer, in case Matika doesn't want to play or have other arrangements.
And Jesse Hughes being a gun fan doesn't make Eden a gun freak too. They make music, they don't shoot together at their spare time.
Wikipedia in my country says Eden left the band , but as you know, anyone can write there, so this is not varified.
Eden has a longer connection to Green Day.
You can see him in this video (also Hans), where he talks about Mike Dirnts equipment at 20:32. The video is from 2013 and I bet my ass Eden knows Billie since more than 20 years.
However it's a really cool thing, that BJA invited him to play, knowing it might be a big part of fighting the trauma that the night at the Bataclan caused.
I don't know if there are side effects from the attacks , but nearly 90 people died at the club, so it's a huge thing.