I would say probably not, unless you have some historical interest in it. Emperor's quick overviews of quantum physics and Gödel might be interesting; they're accessible and somewhat unusual presentations of these ideas. But there are better popular-science books on those topics, such as GEB. The key parts of the argument are frustratingly vague and weirdly coy (while also somehow triumphant).
Shadows... is clearer and more explicit, but I still found it to deliver the argument in much too sketchy a fashion. There's a third book that I haven't read.
The other trouble is that all of these books are already quite dated, in the sense that the biology has been further investigated and we've made a lot of progress in understanding quantum computing since those books.
If you're willing to dive into a little more detail (but still not super-technical), I suggest Scott Aaronson's blog or if you want to dive into the weeds, check out recent debates/papers from Penrose/Hameroff and Tegmark's responses.