That is more than likely the engine vent, it should becoming out of the head somewhere. It's mostly there to prevent overpressure inside the motor and to exhaust various fumes (such as those from hot oil). Normally it's vented into the airbox, and then recycled into the engine and burnt.
It -is- possible for some oil to drip from the tube, especially if the open end is lower than where it connects to the engine. Hot oil can both splash into it, and oil fumes can condense inside the tube itself.
It doesn't sound like they have the optimal setup, you might want to look into finding a crankcase vent filter to plug into the hose. Autozone should have something that might work.