I think it would work. I believe that BioChroma is mainly based in the Spiritual and Cognitive Realms, while at least Steelpushing and Ironpulling are almost entirely Physical. I'd say that an Awakened metal would be able to be Pushed and Pulled, though the Awakened object would probably fight back.
Then again, as Kirkistan mentioned, we're not even sure that Breaths can be stored in metal, and it takes a silly amount of BioChroma to use metal in any capacity, so the odds that the question would be put to the test is slight at best.