We study the impact of imperfect line-of-sight (LoS) phase tracking on the uplink performance of cell-free massive MIMO networks. Unlike prior works that assume perfectly known or completely unknown phases, we consider a realistic regime where LoS phases are estimated with residual uncertainty due to hardware impairments, mobility, and synchronization errors. To this end, we propose a Rician fading model where LoS components are rotated by imperfect phase estimates and attenuated by a deterministic \textit{phase-error penalty factor}. We derive a linear MMSE channel estimator that accounts for statistical phase errors and unifies prior results, reducing to the Bayesian MMSE estimator when phase is perfectly known and to a zero-mean model when no phase information is available. To address the non-Gaussian setting, we introduce a virtual uplink model that preserves second-order statistics of channel estimation, enabling the derivation of tractable virtual centralized and distributed MMSE beamformers. To ensure fair assessment of network performance, we apply these virtual beamformers to the operational uplink model that reflects the actual physical channel and compute the spectral efficiency bounds available in the literature. Numerical results show that our framework bridges idealized assumptions and practical tracking limitations, providing rigorous performance benchmarks and design insights for 6G cell-free networks.