Horsepower requirements vary depending on soil types. Most 3 pt augers use Italian series 1 driveline that is good for 15 hp, with a 45 hp rated gear box. HD augers use Italian series 4 drivelines rated at 36 hp, and a 75 hp gearbox. The tractor will turn it, but the shear pin might break immediately. I had a friend digging with a 3pt unit in shale with a18" auger and could not get anywere due to breaking shear pins, however when he stepped up to a hd unit with larger shear pins he was able to dig the holes.
Then there is the issue of soil type, hard clay can be a pain to drill with an auger without down pressure. 3pt augers are notorious for their ability to spin without making any progress.
To answer ops question: a John Deere 770 can spin a 18" auger. However that does not mean the shear pin won't snap all the time or it will actually dig a hole.