Internet disconnections are not uncommon in Ethiopia but it is far from the end of the world. Despite the alarmist nature of some of the press currently, I don't believe that Addis itself will be significantly impacted. There's just too much shared interest in keeping Addis functioning for anyone including the residents to let things devolve too far.
It may be uncomfortable at times (stock up on movies and shows before you get there to keep you occupied during internet hiccups), get a generator or live in a building with one, make sure you have enough airtime on your SIM card to call internationally if necessary, and remain low-key during the tougher moments should they crop up.
Also, stock up on supplies like water, fuel, snacks, etc. (supply chains in Addis have never been great to begin with), Build a small network of people you trust and can communicate with (domestic help, favorite cab drivers, etc.) Like in most places, don't be an jerk, treat people well (tip well also) and they'll reciprocate.
TLDR: Regardless of what happens, Addis will be fine. It might be uncomfortable at times but Addis tends to swing toward stability despite what's happening elsewhere. Even IF the city gets captured, those doing the capturing will need it too.
Source: been through situations like these in a number of places (including Addis)