The issue you'll have is the cut mark from removing the carpet. When you stain the stairs, this will be much darker then the surrounding wood.
Not necessarily. The knife blade will compress the wood fibers below the cut line and cause the stain to absorb differently in that area. I'd experiment using a wood conditioner on scrap wood before I applied it to the stairs.But that "wood" depend on how deep the cut marks are. If he sands to the depth of the cut marks that will eliminate them all together.