Hell no.
I don't need that moron showing up directly in my feed, nor do I want to contribute to his follower count.
I agree that words are important and reporting on what the President* says (especially with corresponding fact checking and analysis) is important. I follow enough news that I will eventually see his tweets if they're in any way newsworthy.
(I don't buy the "stop reporting his tweets, people will stop paying attention" line that gets tossed around sometimes. Stop reporting them verbatim, if you can't provide any actual analysis on whether his words are outright lies/intentional manipulation. But don't pretend that the tweets don't matter.)