I always thought that if I use a grid on a softbox with a diffuser, or beauty dish with the sock on, then it is necessary to put the grid only after the diffuser/sock. Otherwise, the grid has no effect. But actually never tried it in practice. Recently I came across lighting tutorial where the coach put the sock on to a gridded beauty dish. Was it just a shortcut to save a couple of seconds (in order to avoid putting the grid off the dish)? Or does it really have an effect on the light quality?
Depending on the dish shape and the diffuser material, it could conceivably make a perceptible difference if the light is used in very tight.
"Beauty dish" refers to a whole host of different reflector styles, from the even parabolic Elinchrom to the step-sided Mola to a basic flat-bottomed, high-sided design that looks for all the world like a minimalist Bundt pan that's missing the centre column. There could be a "ring" shape that's preserved at the diffuser when using a grid before that would be smoothed out without.
But, as you may have guessed, that's really reaching for an answer to your question as asked. A better question would be "is there any good reason to take the time to remove the grid before throwing on the sock?" There, the answer is probably no unless the dish was used in very tight (relative to its diameter) with a glossier-than-average subject. If the photographer works in a sort of binary gridded-or-diffused mode with the dish, there's probably no good reason to bother installing and removing the grid over and over (which gets more fiddly, and more prone to dropping or bending the grid, as the size of the reflector goes up). Grids aren't as cheap as they might be, so why risk damage when you don't have to?