With the increasing penetration of voltage source converters (VSC) in the modern power grid, the transient stability of grid-following converters has attracted extensive attention. During grid faults, instabilities of the grid-following converter might happen which mainly originates from the phase-locked loop (PLL) being not synchronized with the grid. In the existing research, current dynamics is considered to be very fast and its effect on the transient synchronization stability can be ignored. However, in the case of high-power converters used for large wind turbines, the bandwidth of the current loop cannot be designed too high due to low switching frequency. Neglecting the coupling effect on the synchronization stability will lead to wrong conclusions. This paper firstly proposes an improved equal-area criterion to show that the current dynamics change the accelerating and decelerating area and might deteriorate the stability, which reveals that the coupling effect of current and PLL is non-negligible. Accordingly, a refined fourth-order nonlinear model is proposed to describe the coupling effect of the current loop and PLL, which is utilized to give the bandwidth boundary whether the current dynamics can be ignored. Simulations and experiments are performed to verify the correctness of the proposed nonlinear model.