Is "get passing grades and follow voraciously your curiosity on the side" a good strategy for graduate school?
The passage you have shared refers specifically to a baccalaureate degree:


  The edge, I realized, isn’t in the package of what was on the official program of the baccalaureate... but exactly what lay outside it.


In a PhD, coursework takes a backseat to research. In research, there is no such thing as "get passing grades"; there is no meaningful threshold at which your research is considered acceptable, only a continuum of poor to exceptional. At the end of your PhD, your prospects on the job market (especially the academic job market) and the impact you have made with your work depend on how close you are to the "exceptional" end of that range, not just having achieved some minimum requirements and earned a piece of paper that says you have a degree. 

Furthermore, PhD-level research requires a level of depth and focus that is not typically present at the undergraduate level.

That's not to say you can't have broad interests, and you can even leverage your broader interests to improve the quality of the work you do in your primary field. But a strategy of planning to undertake a PhD and put minimum effort into your PhD research while doing other things on the side is not a winning strategy for most people. Instead, you should try to use your curiosity for your PhD research. (Also see: Can I slack off and get a PhD?)

In fact, later in that same chapter, Taleb describes how his curiosity and drive to understand probability led him to specialize in that and focus on that to the exclusion of everything else:


  When, at Wharton, I discovered that I wanted to specialize in a profession linked to probability and rare events, a probability and randomness obsession took control of my mind. I also smelled some flaws with statistical stuff that the professor could not explain, brushing them away—it was what the professor was brushing away that had to be the meat. I realized that there was a fraud somewhere, that “six sigma” events
  (measures of very rare events) were grossly miscomputed and we had no basis for their computation, but I could not articulate my realization clearly, and was getting humiliated by people who started smoking me with complicated math. I saw the limits of probability in front of me, clear as crystal, but could not find the words to express the point. So I went to the bookstore and ordered (there was no Web at the time) almost
  every book with “probability” or “stochastic” in its title. I read nothing else for a couple of years, no course material, no newspaper, no literature, nothing. I read them in bed, jumping from one book to the next when stuck with something I did not get immediately or felt ever so slightly bored. And I kept ordering those books. I was hungry to go deeper into the problem of small probabilities. It was effortless. That was
  my best investment—risk turned out to be the topic I know the best. Five years later I was set for life and now I am making a research career out of various aspects of small probability events.