I think working together with the League but not being a direct part of it will probably be a common stance. I don't know if my character idea would fit into the League itself, all that well, since Justice League Dark literally was made for characters like him. Though, either way, I wouldn't mind having something like the JL being in the center of the story. 

I personally really like sandbox-type RPs, they just require all the members to actually be active and not wait for the GM to hand-hold them through everything.