Underwater optical wireless links have limited range and intermittent connectivity due to the hostile aquatic channel impairments and misalignment between the optical transceivers. Therefore, multi-hop communication can expand the communication range, enhance network connectivity, and provide a more precise network localization scheme. In this regard, this paper investigates the connectivity of underwater optical wireless sensor networks (UOWSNs) and its impacts on the network localization performance. First, we model UOWSNs as randomly scaled sector graphs where the connection between sensors is established by point-to-point directed links. Thereafter, the probability of network connectivity is analytically derived as a function of network density, communication range, and optical transmitters' divergence angle. Second, the network localization problem is formulated as an unconstrained optimization problem and solved using the conjugate gradient technique. Numerical results show that different network parameters such as the number of nodes, divergence angle, and transmission range significantly influence the probability of a connected network. Furthermore, the performance of the proposed localization technique is compared to well-known network localization schemes and the results show that the localization accuracy of the proposed technique outperforms the literature in terms of network connectivity, ranging error, and number of anchors.