It's worth mentioning that in human history, warfare has often been a driver of technological innovation, from the stirrup to the nuclear bomb. So it doesn't really follow that a warrior culture would be incompatible with technological growth. Presumably Klingons would constantly be trying to think up better ways to kill each other.
However, their class system could get in the way of innovation, if the dominant warrior class did treat scientists and engineers with disdain. There have certainly been cases of that in human history -- for instance, in slave-owning ancient Greece, they made great intellectual progress, but because physical labor was disdained as a low-class activity, they didn't apply that intellect to technological innovation and thus missed the chance to have an industrial revolution millennia ahead of the one we got. We know from ENT: "Judgment" that as recently as the late 21st or early 22nd century -- during Advocate Kolos's lifetime -- Klingon society was more balanced between social classes, but then the warrior class took over and marginalized other classes such as scholars, engineers, jurists, etc. And we've seen abundant evidence that the warrior class has an often excessive devotion to tradition, e.g. using swords in combat against foes armed with energy weapons. (Haven't they ever heard that you're not supposed to bring a knife to a ray-gun fight?) So it's certainly possible that they could've marginalized scientists and engineers out of their ideological narrow-mindedness, and thereby slowed the rate of technological progress in the Empire.