Q.New Guinea impatiens
Can they grow successfully in a shallow planter with soil only about 4″ deep?
4 inches is very shallow. I would suggest that the minimum depth of 6 inches would work, but 8 to 12'' would give the plants a much better planting depth.
The more shallow the container, the more often you will need to check watering, and if the plant becomes quite root bound the plant may not be at it's best.