Definitely not in current shape, as it depends on tightly packed soil/rock to provide an opposing force to resistance of the ground/rock against the drill. Asteroids, with low gravity, will be far less stable and this sort of forces could easily break apart smaller ones.
Also, starting the tunnel would be a serious problem, as instead of 1g to keep the equipment stable on the ground, it would require active thrust or some sort of anchor system to initiate the tunnel - otherwise the drill will just send the whole machine flying away from the asteroid.
Then there's the whole slew of smaller problems - screw conveyors for loose material depend on gravity to keep it from spinning uselessly around instead of being moved. Cooling - only radiative; coolants like water are expensive and scarce. All bearings, joints, actuators, contact surfaces etc need to be passivated against cold welding. Common lubricants like grease need to be replaced with stuff that works in vacuum and temperatures of space. The tunnels on Earth are to be reinforced with concrete, not really a material you can manufacture in bulk in space; it won't bind in vacuum (where all the water will either freeze or boil off). With no air to slow down debris that get smashed by the machinery, they will keep flying like shrapnel until they bounce off different surfaces enough to come to a rest. There are countless other similar "small things" - none of them impossible to overcome alone, but the sheer number completely overwhelming.
The concept has some merit, but it's not 'pack a machine on a rocket and drill some tunnels' thing. Such a drill would need to be very thoroughly redesigned to be usable in space.