Title says it all, I don't see confirmation in this question and a cursory google search seemed to say assume no and speculate about the pokemon bank.
According to this image:
Pokemon Bank will receive an update for compatibility with Pokemon Sun/Moon in January 2017, but you will be able to trade Pokemon from 6th gen to 7th gen only, and not back.
As you can read in the white box:
Pokemon not sent to Sun/Moon can continue to be used in X/Y or OR/AS.
Source from Pokemon official site.
Pokemon Sun and Moon are not compatible with the Generation 6 series of games: Pokemon X and Y; and Pokemon Omega Ruby and Alpha Sapphire. You won't be able to trade or battle between these games and Pokemon Sun and Moon, therefore you'll need a special app called the Pokemon Bank to transfer your Pokemon.