Push processing has different effects on B&W, Color Negative and Color Slide Film.
Pushing does always mean: longer development times. A longer development time produce coarser grain and thus reduces resolution slightly. Resolution might have an impact on sharpness, depending on the enlargement factor and the viewing distance. However, it normally does not produce less sharp B&W negatives. Coarser grain might even increase the perceived sharpness of an image.
Color Negative and Color Slide Film do not have grain at all. The bleach-fix-process (whether in one or two process steps) eliminates all silver grain. What is left are dye clouds produced during color development. These dye cloudes do have less sharp contours than silver grain. And larger dye clouds might look more fuzzy.
Color Negative Film is not suited for push processing, since the development of silver grain and dyes take place in one step. Pushing a Color Negative Film causes crossover effects that cannot be filtered properly during printing. This is because the color development process has different effects on the different (color) layers of the film.
You may push Color Slide Film, because the development of the silver grain and the color dye development take place in two different process steps. However, pushing a Slide Film too far increases the base density in the first development process and will lead to less black shadows in the reversal process. Reduced saturation is a problem of color side densities. Pushing a film increases contrast and thus increases the effect of color side densities.