Obviously there is a chance it works and a chance it doesn't, and every fish is different, but...
I am going to disagree with Dmorty217. If it works short term, I think that is just as good as having added them at the same time. I've never seen anything work short term that doesn't work long term except when the fish get bigger. I have seen things that don't work short term eventually work out long term.
A 375g is a big tank, and I can say from experience that a lot of combinations that didn't work in a 120g works very well in a 270. My guess is you'd be okay.
I believe (correct me if I am wrong) that all tangs shoal in the wild and travel long distances rather than keep a territory like damsels, angels, etc. They will probably be okay as long as they can maintain enough distance.