Yes, it is. Why did Joseph travel to Bethlehem with his betrothed Mary, who was pregnant at the time? Perhaps Luke 2:4-5 can give us some insight: "And Joseph also went up from Galilee, out of the city of Nazareth, into Judaea, unto the city of David, which is called Bethlehem; (because he was of the house and lineage of David) To be taxed with Mary his espoused wife, being great with child." Joseph was going to Bethlehem to be taxed, a tax which was first made when Quirinius was governor of Syria, and was accompanied by his espoused wife who was great with child. What possible conclusion fits the narrative other than that it was taking place while Quirinius was governor?