Can I print with UV curable inks even though I do not have a UV curing unit?

No, that would not be possible. You must cure our UV inks in a commercially manufactured UV curing unit that has been specifically designed to generate the proper amount of energy and wave length necessary to induce polymerization of the ink film. UV light bulbs or sunlight may cure the ink somewhat over time, maybe to a "dry to the touch finish" however, the ink film will never become completely cured and adhesion to the substrate will be compromised.