I'm learning by myself =p
I think it would be useful to frame the discussion around the understanding that "without a teacher" can mean (1) no teacher currently, or (2) never had a teacher. It's an important distinction.Also, it would only be in a perfect world that all teachers are competent, helpful or suited to teach any level of advancement. They're not, and that's important as well.
Your subject line asks... can you teach yourself to play any piece to a professional standard.... within reason... yes.....
Is it a good idea, if your goal is to play pieces to a very high standard, to not have a teacher? Absolutely not. It's even a fairly bad idea. A teacher, even an average one, WILL speed up the learning process. And it will speed it up by a great deal.
[...] if you are good, a teacher can only make you better.
That presumes that the teacher, too, is "good"; a bad or mismatched teacher, on the other hand, is likely to have the opposite effect.