Yes, this is a perfectly normal practice, still used, especially for tight spaces, as seen in this video moving a 747 into the hangar for service. And no, it doesn't require any special equipment - the nose gear attachment is designed to be used either way.
While it's uncommon, it appears that many pushback tugs are specifically designed to fit underneath an aircraft like this. This wiki notes that (emphasis mine)
Pushback tractors use a low profile design to fit under the aircraft nose. For sufficient traction, the tractor must be heavy, and most models can have extra ballast added. A typical tractor for large aircraft weighs up to 54 t (120,000 lb) and has a drawbar pull of 334 kN (75,000 lbf).1 Often, the driver's cabin can be raised for increased visibility when reversing, and lowered to fit under aircraft.