There's a lot of things that go by the name "continental philosophy." Critical Theory is probably one of the ones were knowledge of basic formal logic would be useful. For some of the other more famous figures in contemporary continental philosophy, you don't need to know any formal logic or math.

To be honest, depending on what you mean by "math", you don't need to know much of it to do most philosophy -- continental, analytic, personalist, or any other contemporary school.

Regarding your characterization of critical theory as seeking a more "pragmatic research methodology," I am not so sure that's an accurate or fair characterization. I might say it seeks a more ideologically-driven research methodology than the status quo. And pragmatism admits at a minimum two diverging definitions -- (a) closer to Pragmatism (the American philosophical school) and (b) practical.

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But seriously, it's unwise to restrict your readings to just continental philosophy -- or even just analytic philosophy. Read good philosophy that makes solid arguments. Much of the best analytic philosophy is informed by the history of philosophy. And much of the best continental philosophy is in dialogue (and I don't mean the way Derrida was) with contemporary analytic philosophers and the history of philosophy. 

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As an addendum, I write this not as someone unfamiliar with continental philosophy but as someone who earned an undergraduate degree in philosophy from a US institution that included continental philosophy in what was taught. I then earned an MA from a continental/historical program in the US and finally a PhD from a program strong in continental writing under an advisor who is moderately well-known in continental circles.

While I don't make contemporary continental the primary focus of my research at this point, I do have multiple published articles that compare 20th century continental thought with 19th century continental thought...

I *strongly* advise against neglecting other forms of philosophy and against not developing your skills in broad areas of philosophy.

or to word this in a completely different way -- please look up what the big continental figures actually studied when they were students. E.g., [Martin Heidegger studied John Duns Scotus.][1] Foucault and Sartre both studied Hegel.


  [1]: http://en.wikipedia.org/wiki/Martin_Heidegger