Promotions: There are generally no promotions above the MTS level at Avaya. Promotions to DMTS are extremely rare, but it means beyond exceptional performance YoY for at least 5 years in a row. In ten years, I have seen only 1 person earn a promotion to CMTS and 2 earn DMTS. Also: there are also two pay plans. Be careful when changing between the two because the DMTS can be easily lost when going back and forth between the same pay grade in the "Management Pay Plan" (MGR) and the "Techncial Pay Plan" (MTS/DMTS).
Politics: I would compare the politics at Avaya to that of the U.S. Congress. It is extremely political and your success or failure rests upon your ability to navigate the political waters. It is very doable, but it takes a certain savvy as well as a certain type of personality.