Adding x ppm of co2 will lower the pH by x amount no matter what the hardness of your water is to start with. A tank with sufficient injected co2 will be about 1.0 pH lower than if the tank had no injected co2. So if you are starting with 8.0 pH, after you inject co2 you will be down to 7.0. If you start at 7.0, you will go down to 6.0. Hardness does not change this calculation.
However, this type of pH change is not the same as changing pH via other methods. It can fluctuate quite a bit if co2 fluctuates and the fish seem unaffected. Fish that like lower pH usually also like softer water, and adding co2 does not change your hardness, therefore it doesn't change the type of fish that will do well in your water...if you have hard water, choose fish that like hard water/higher pH. Co2 won't matter.
However as has been mentioned, fluctuating co2 is a terrible thing for plants. It's better to have no co2 injection than to have it fluctuating. Reason being that plants adapt to higher co2 levels when exposed to it. When suddenly co2 drops, the plants cannot adapt quickly, and therefore cannot get enough carbon anymore. This leads to a whole host of problems related to the carbon deficiency your plants will then experience (since carbon is the major thing that plants are made of....if they can't get enough, they can't grow or repair themselves), including algae, leaf loss, holes in leaves, and sometimes just total die off especially with faster growing plants.
In general, hard water is better for plants than soft water, as it contains more of the things plants need (such as magnesium, calcium, iron, etc.). Some plants are an exception to this though so research your plants before you get them.