Oh yeah, I just remembered SWORD is a thing in the comics. I wouldn't be surprised if Fury starts that up to combat cosmic threats in the future while the Avengers handle Earth stuff.
Nope, SHIELD has been public again since early in season 4 of Agents of SHIELD.
But we also don't know if he's actually playing a SHIELD agent in this. They could be using the character and giving him another role. I do hope he's a SHIELD agent though.