Nah, they should be slotting Green into the middle order. Burns can't buy a run and needs to go. Also, not sure where you get the idea he made 180 in his last test. He made 18 and 40 in his last test match against NZ. The test before that he made 0 and 35 and the test before that he made 9 and 53. Against Pakistan he scored 97 in his only innings in the first test, but only made 4 in his only knock in the second test. Did nothing much in England either. I think you're thinking about a match against Sri Lanka on an absolute road almost two years ago. I don't think Warner will play, so he'll probably be getting a reprieve for at least one more test, but he has been far from setting the world on fire since that knock against sri lanka and his first class form has been abysmal.
Pucovski and Green should both play.....not that I thinbk that is likely to happen.
Slight revision - Burns did miss the ashes, I forgot about that.....but he 100 percent played against NZ and Pakistan and with the exception of two innings, his returns were very modest.