Major Nelson specifically addressed people with chat and connection issues being a top priority. It was taken as "confirmation" of mortiner's 'Xbox live totally broken, getting overhauled in a year' rumour though.Never had NAT issues on 360. Can't play. Multiplayer or do party chat on XB1. Nothing is being done about it.
So yeah, they're aware there's issues. I had a strict nat, fixed by turning off upnp on my router.