The correlation runs the other way: they produce manifestos in order to make the events look more convincing and polarize people. (I.e. it establishes the connection between far-right politics and mass shooting, so as to stigmatize right wing political views altogether.) The concept of a shooter leaving a manifesto originates from the Breivik attack, which was a psy-op.

So the very mention of a manifesto is what increases the likelihood of this shooting being fake.