The twist should reduce the cross section area and so compress any core, not put it in tension., which is good since E/g is much stronger in compression. But the E/G is still weaker than the steel around it an dthe peripheral tube will carry the majority of the load.
You could use a weaker tube and rely on compression of the core or greater core strength to contribute to the total strength - but why would you? Steel is a $1 or even 0.50c a pound. E/G is more expensive.
E/G has it's place but you can't expect to do everything with one material.