Apparently, it is qute possible. You might want to look up hardwood cuttings vs softwood cuttings. If the branch has been around for awhile I would take a fresh cutting. Here is the procedure.
Dogwood: How To Grow a Dogwood Tree From a Branch
Like every other tree propagation process, a Dogwood tree from a branch must be healthy to propagate successfully. It also needs to be at least 12 inches long and has a diameter of about 1/4 to 1/2 inches.
The cutting angle is also 45-degree, and all the leaves or buds should be removed from the lower half of the cutting.
The rooting hormone will stimulate root growth, and you can plant the cutting, moist and well-draining soil away from direct sunlight.