Yes, you can apply polyurethane on an unfinished hardwood floor. You can do this with the help of a fine brush, cloth, or foam pad. This polyurethane layer on the surface of an unfinished hardwood floor provides it a protective layer. This protective layer can stop water from entering the hardwood. It acts as a defender for your hardwood floor against water damages. If you apply it over an unfinished hardwood floor, then you should also recoat it after completing the installation of the hardwood floor to make the floor last even longer.