The widely deployed grid-following converters (GFLCs) may lose synchronization under grid disturbances, presenting a critical challenge to the power electronics penetrated power grid. While some methods have been proposed for analyzing the transient synchronization stability, their models tend to assume an ideal current loop. Using a full-order system model, this paper demonstrates that the nonideal current loop significantly weakens the stability of GFLCs. Specifically, the basin of attraction gets decreased and more sensitive to parameter changes. The complex bifurcation behavior behind these changes is revealed via the numerical continuation. Accordingly, a design principle is derived for enhancing the transient synchronization stability.