Can a gas additive mess up my car if not driven much after its been added?

About a week ago I added a bottle of some sort of gas additive(I think it said it would keep my engine dry or something) that I found in my garage which means it was old, but it was unopened. My car seemed like it did run better but I only drove it for about a minute to get home and than I turned it off and didn't touch it for about 3 days. When I went to start it the engine didn't do anything at all. The battery worked but the engine didn't really try to start at all.Could this be from not driving the car much right after adding this?