Mount ceiling fan without electrical box
Electrical boxes serve several functions. They protect wiring where insulation has been removed. They prevent inadvertent contact with exposed components. They contain sparks when the worst occurs. And they provide standard mounting points for fixtures. 

I'd be inclined to "code things up" with a wraparound box like so:




  Nonmetallic ceiling joist box for ceiling fans. 4'' diameter x 2 1/8'' deep, 12.0 cu. in. 4 clamps, 2 1/2'' knockouts. Maximum fixture weight is 150 lb., maximum fan weight is 70 lb. Exceeds National Electrical code requirements. Recommended for earthquake areas.