Because a salt finish leaves pits in the surface of the concrete, debris is likely to collect in the depressions. This debris may consist of leaves, dead insects and dirt. When left to decompose, this material will stain the surface of the concrete both inside and around the pits. If you wish to avoid this, you can clean the surface regularly and make special efforts to remove all material that has collected in the pits.
Concrete that has color added during the mixing process creates a surface that will resist discoloration even if chipped. However, color-mixed concrete is especially prone to discoloration while drying and setting. To achieve the most uniform coloring possible, manufacturers provide many rules for how to handle the concrete as it dries. These include not over-troweling, as this can create color burns, and not coating tools with water because this will fog or discolor the concrete. Although these rules do not specifically advise against using salt on the surface of colored concrete, the sensitivity of colored concrete to water suggests that a salt finish would be likely to change the color of the concrete in unpredictable ways.
Concrete can have acid stain added after it has dried, and even several years after the concrete has been in use. Acid stains soak into the surface of the concrete at about the same rate as water, and so if the concrete has a salt finish and you have noticed that the pits absorb water more readily than the rest of the concrete surface, you can expect the acid stain to do the same. This will lead to darker areas around each salt pit and the effect can be similar to natural stone.
Acrylic colors can also be applied to concrete that has dried and been in use for years, but the color options available are much more vibrant than acid dyes. The color of an acrylic stain is not caused by a chemical reaction as with acid dyes, and so the uniformity of the color is much greater. However, the depth and tonality that can be achieved with an acid stain is difficult to mimic with acrylic color. If you prefer color coverage that is consistent over the surface, even with cracks and pitting, staining with an acrylic dye is the best option available.