The relationship discussed in the literature mostly involves them as two competing explanations for underachievement. Learned helplessness is about internalizing the conception of yourself as worthless; self-handicapping is about trying as hard as you can to avoid viewing yourself as worthless. The studies I could find in ten minutes on Google Scholar mostly suggested a current consensus that run-of-the-mill underachievers are sometimes self-handicappers but not learned-helplessness victims - but ten minutes does not a literature review make.

Oh, and thank you for linking to that Wikipedia article. The sentence about how "people performed mental tasks in the presence of distracting noise...if the person could use a switch to turn off the noise, his performance improved, even though he rarely bothered to turn off the noise. Simply being aware of this option was enough to substantially counteract its distracting effect" is really, really interesting.