If you're in a confined space in Ultra Sun/Moon or Sun/Moon, and get on Tauros, you'll move sometimes. If you have an egg in the party, and it needs one more step to hatch, will it hatch?
No. Tauros micro-adjusting on the spot won't work. However, the small square south of the day care will work if you hold B and move your circle pad in a circle (thanks to The Poipole for this).
Major edit: I just hatched a Jangmo-o egg that was in my party by pushing against a wall while riding on Tauros! What you are asking is true.