For me, at 17 when I read it, math was just a bunch of symbols and exercises. It introduced me to logic and reasoning, made me think about the world differently.
It's like the real red pill in the matrix that's not just something you swallow. You think about it, and you start wondering what else you think you knew about math and the world can be challenged.
It made me a braver man. In that sense, it did change my life.
I think if your mind isn't changed after reading about these figures, then you haven't really gotten it.
Hofstadter isn't necessarily the main attraction here. He created a framework (ie the structure of the book) where these subjects can be reasoned about.
Admittedly, I read it in formative years, but until I read GEB, I didn't really grok what "genius" meant. Understanding strange loops in context of great thinkers who expressed it, and seeing strange loops as the nature of consciousness, and wondering how it could be expressed in software... blew my mind, in several senses of the phrase.