You "leaking big time" is not happening from that hose and yes, it is an overflow/pressure drain hose. IF you "overfilled" the reservoir to the top, you will see some coolant come out there or if the pressure builds too high for any reason, it bleeds there. If I remember right, and I just went to look, on the front side of the reservoir bottle there is a steel clip that acts as a shelf for that hose to lay in and store there. It is right under the front seam of the bottle. By front I mean the long side of the reservoir bottle that faces the front of the vehicle. In you picture you can see part of that clip, right next to the edge of the air filter housing.