Note that gradient layer styles can’t be dithered, and gradients in placed
objects (such as stuff you’ve pasted from Illustrator) aren’t dithered.
If you use transparency in a gradient, that won’t be dithered either, which
can be a huge issue at times. There is a solution for some specific cases: if
you’re using a gradient with transparency to lighten an area with white,
then using a non-transparent gradient with a Screen Layer blending mode
will let you dither it. The same technique can be used for darkening with
the Multiply blending mode.