This paper delves into the dynamics of resource allocation in ultra-dense Low Earth Orbit (LEO) satellite networks within a cell-free massive MIMO framework, focusing on the impact of residual synchronization errors. We conduct various analyses to understand how these errors - encompassing time, phase, and frequency - influence the Signal-to-Interference-plus-Noise Ratio (SINR) and the average number of satellite links connected to each user. Our approach measures the effects of these remaining synchronization errors and uses these values to inform and optimize power and resource allocation decisions. The study reveals that as synchronization errors increase, the number of effective satellite links to users diminishes, consequently reducing the number of satellites actively connected to each user. This research not only highlights the critical impact of synchronization errors on network performance but also demonstrates how advanced knowledge of these error variances can significantly enhance resource allocation strategies and network efficiency in future ultra-dense LEO satellite systems.