I think what giant-fan asked you about Black Bolt being an Avenger because he's an Illuminati can be extended to this one: "Can the Illumianti be considered Avengers?" Because although they star an Avengers title, they actually aren't Avengers. Most of their members aren't Avengers, they're a super-secret-Cabal, they have ties with the entire MU, not only the Avengers, etc. In an out-of-universe perspective (ours) they can be considered Avengers, but in-universe they just can't, right?
In-universe the ones that aren’t on the Avengers’ roles wouldn’t be on the Avengers’ roles–but that’s pretty much just Black Bolt at this point.