Maintaining reliable Vehicle-to-Satellite (V2S) connectivity for critical mobile services is a significant challenge for Low Earth Orbit (LEO) satellite constellations due to high orbital velocities and frequent radio obstructions in urban environments. Spatial diversity through multi-link connectivity -- the use of multiple simultaneous satellite links -- can mitigate these shadowing effects, but introduces a potential increase in signaling overhead via frequent Handovers (HOs). This paper investigates this fundamental trade-off by evaluating three HO mechanisms. Leveraging a high-fdielity simulation framework that integrates orbital dynamics, vehicle mobility, and urban geometry, we analyze the impact of using up to three parallel links on the satellite link availability and HO frequency. Our results demonstrate that while multi-connectivity effectively mitigates obstacle blockage, the magnitude of the reliability gains and the associated signaling costs are strictly dependent on the HO logic. These findings establish a baseline for future works, including more detailed channel models and real-world scenarios.