No. We're using the low heat setting for one hour, which is just long enough to warm the mulled wine. Unless you're bringing your mulled wine to a rolling boil on the stovetop for a significant amount of time, the alcohol will not cook out. A study was done by Idaho State University where they concluded that alcohol does not cook off as quickly as we think. Boiling alcohol, uncovered, for 15 minutes straight would still retain 40% of its alcohol content. To cook the alcohol out entirely, it would take about 3 hours. For this recipe, your wine stays covered the entire time and never comes to a boil.