In which case, it depends on the type of inhibitor. A competitive inhibitor has a structure similar to the substrate, hence would bind to the active site as well, competing with the substrate for the enzyme active sites, decreasing enzymatic activity. A non-competitive inhibitor binds to the allosteric site of the enzyme, causing a structural change in the enzyme active site shape.
There's a difference between the effects of cold-brewed coffee vs. hot-brewed coffee: because different chemical reactions are achieved at higher temperatures, cold-brewed coffee will have a smoother caffeine effect and overall less acidity, which some people experience as part of the kick..
The study, which appeared in the Archives of Internal Medicine and got a lot of buzz, suggested that women who drink coffee have lower rates of depression. Depression risk was lower for women who drank more coffee (over two cups daily) than for those who drank one cup or less per week. It was an association, so that doesn't prove that coffee was responsible for the lower rates of depression, but it was a very large study (more than 50,000 women) that traced coffee intake and depression diagnoses over the course of 14 years.