Yes bacon grease can start a fire in the oven if you do not clean up the bacon grease and allow it to accumulate in the oven especially near the heating element or if you just allow the bacon grease to accumulate in the oven if it's a gas oven.
The heat will usually cause the grease to smoke and then burn off the oven and will usually not catch fire in small amounts of bacon grease due to the lack of oxygen in the oven due to the door being closed.
However still a fire can result but mostly it will extinguish itself.
When you bake bacon in the oven or other foods you should clean the cooking oil or bacon grease out of the oven after the oven cools down.
That will prevent the buildup of the grease and cooking oil and prevent a fire or smoke in the house.