No, divertare always takes essere as it's auxiliary. http://www.wordreference.com/conj/ItVerbs.aspx?v=diventare
There is a slight difference in meaning between "What will they become?" and "What will they have become?". The latter is something that will happen after a specific time or event in the future. The question alone sounds odd, but if more information is added it gets more sense. For example: "What will they have become after passing through that?" Another possible translation to English is the conjectural use, as GregHullender suggests in a comment above: "I wonder what they have become?"