It varies. In some cases it can speed things up, and in others it can reduce performance. You need to test for your specific usage, on the hardware that you care about, and see what happens.
One way it can speed things up is when you're hitting memory bandwidth limits on writing to the frame buffer. In my experience this mostly affects lower end graphics cards. In those cases using discard to implement an alpha test so you don't write out fully transparent pixels can improve performance. This might apply to the rendering of a particle system, for example.
On the other hand, in shaders that write to the depth buffer, using discard can hurt performance. This is because using discard has a side effect of disabling some of the hardware's depth buffer optimizations, because it makes the depth output of the shader impossible to predict before the shader runs. Disabling those optimizations can make future draw calls go more slowly, especially ones that would fail the depth test.
In addition note that enabling alpha blending can also have a performance cost - it uses more memory bandwidth than opaque rendering, because it has to do a read-modify-write of the frame buffer instead of just a write.
