A reconfigurable intelligent surface (RIS)-assisted non-orthogonal multiple access (NOMA) system is investigated, where the transmitter (Alice) is a dual functional radar communication (DFRC) base station (BS) that aims to sense the location of a potential warden (Willie), while simultaneously transmitting public and covert signals to the legitimate users, Carol and Bob, respectively. Both cases of known and unknown Willie locations are considered. For the known-location case, assuming perfect channel state information (CSI) at Willie, a covert rate maximization is formulated with the joint optimization of active and passive beamforming, which is solved using successive convex approximation (SCA), penalty method, and semidefinite relaxation (SDR). For the unknown-location case, we propose to estimate Willie's location via radar sensing and develop a sensing-based imperfect CSI model. In particular, the CSI error uncertainty is bounded by the sensing accuracy, which is characterized by the Cramer-Rao bound (CRB). Subsequently, a robust communication rate maximization problem is formulated under the constraints on quality-of-service (QoS) of Carol, sensing accuracy, and covertness level. The Schur complement and S-procedure are employed to handle the non-convex constraints. Numerical results compare the system performance under the two cases, and demonstrate the significant covert performance superiority of the sensing-based imperfect CSI model and NOMA over the general norm-bounded imperfect CSI model and the orthogonal multiple access scheme. Furthermore, the dual yet contradictory effects of sensing on covert communications are revealed. It is also found that Alice primarily utilizes Carol's signal for sensing, while allocating almost all of Bob's signal for communication.