Identifying vital nodes in complex networks is critical in various research areas, including social network analysis, epidemiology, and physics. Centrality measures are commonly used and combined for this purpose. However, the impact of growing privacy concerns on the identification of vital nodes, particularly in networks containing sensitive data like Bluetooth-based contact networks, is not well understood. Our study evaluates the effectiveness of vital node identification algorithms under privacy-preserving network settings. Through simulations, we identify algorithms that are most effective for estimating node vitality when only limited network information is available. Furthermore, we demonstrate that machine learning models provided with aggregated output of the most promising approaches and trained with only 20 percent of the data can significantly outperform state-of-the-art approaches, especially when network information is strongly limited. This research advances the understanding of privacy-centric approaches in complex network analysis and shows how machine learning-based methods can empower advanced network analysis under privacy-preserving conditions.