I don't think anyone on here can answer this in a historical way — you're asking a psychological question about a very disturbed man. But I will say: have you ever tried to write a manifesto that doesn't sound like you, on a topic you care about, such that someone who has known you a long time and heard you talk and rant at length (like your brother, who was who identified the letter) would not be able to recognize it? We all write in definable styles, especially if we are not people who take extreme care with our writing (my over-use of parenthetical statements, for example, is a pretty definite writing tic). Can one write like someone else? Sure, but it's takes immense effort and arguably some careful self-awareness. The sort of thing that one might not expect a mentally ill fanatic to have. One can be great at one domain (sending mail bombs) and very poor at another (composing a manifesto).

Even if Kaczynski had masked his writing style (very difficult), if his manifesto was to have any genuine and specific content, it would be potentially identifiable. If I re-wrote his manifesto in my own words, it would still be a very strong anti-technology screed with a lot of other themes running through it — potentially something that could be identified by someone who knew its contents, and its writer, very well.

Separately, I would note that if you do study people closely, you find that they do use pretty identifiable mannerisms (I have found Truman's "Trumanisms" — specific turns of phrase that he frequently used — to be a way to identify when he had input into speeches that were written in his name, for example). We all do. Sometimes we're self-aware of them (I try to be), sometimes we don't.

Unhistorical anecdote: when I was in my teens I suffered a concussion that gave me amnesia for several hours. It caused my short-term memory to clear out after some amount of time, and my memory would basically be "reset." According to those with me (I have no memory of this), I would ask exactly the same sequence of questions over and over again, until finally my short-term memory came back (I remember only the last version of each question). So much for creativity and free will!