Yes, you can place a refrigerator on top of luxury vinyl plank flooring, provided the installation was executed properly as a floating floor with correct expansion gaps or fully glued down. Because refrigerators are extremely heavy, you should place protective furniture sliders, thin hardboard, or appliance rollers under the feet when moving the unit in or out to prevent gouging or tearing the wear layer. Distributing the weight evenly ensures the locking mechanisms do not separate under heavy localized loads.