Not exactly. Without the feeling of drowsiness that signals drunkenness, people are fooled into thinking they're more sober than they actually are. As a result, they are at a greater risk of harming themselves.
The cocktail is also potentially dangerous to your health. The combination of alcohol and a stimulant can cause shortness of breath and elevate heart rates to unsafe levels. (By "stimulant," we're talking drinks with high caffeine content -- this includes coffee as well as energy drinks.)