A mouthpiece yes, but an official way to "make policy" no. Policy is still created through official means like signing executive orders, etc.
These statements can have legal power behind them such as declassifying documents.
Sorry but you are wrong. Trump's administration has stated that his tweets are official statements. Meaning, he can't block people who reply to his tweets.
https://www.cnn.com/2017/06/06/politics/trump-tweets-officia...
https://twitter.com/RealPressSecBot
For those who don't want to click, it collects Trump's tweets in real-ish time, and reframes them into images of official-looking messages. The latest one as of the time I post this comment begins:
THE WHITE HOUSE
Office of the Press Secretary
FOR IMMEDIATE RELEASE
May 23, 2018
Statement by the President
And then puts the text of Trump's tweet immediately below.https://twitter.com/RealPressSecBot/status/99928406869604761...