Seems to me the problem here isnt a coach having Twitter but rather a bad coach having Twitter.
Any time a coach who isnt well liked by the fanbase puts himself out in public, he risks getting a negative reaction.
Can Tom Crean tweeting backfire? Sure. Tom Crean walking into a local gas station in Indiana could also backfire. The expectations there are ridiculous and he isn't performing.
If done correctly, a coach can use Twitter to promote a positive face for the program.