The data-driven approach is promising for computationally efficient modeling of optical fiber channels. Here, for the first time to our knowledge, we investigate the impact of the input optical signal-to-noise ratio (OSNR) on the accuracy of data-driven modeling for optical fiber channels, based on a conditional generative adversarial network (cGAN). Initially, considering a single span of 80 km of standard single mode fiber (SSMF), we vary the launched optical power for the ease of emulating both linear and nonlinear transmission scenarios. When the input OSNR of a root raised cosine (RRC)-shaped 16 quadrature amplitude modulation signal with a roll-off factor of 0.1 varies, we identify that there occurs an OSNR threshold for accurately modeling a single span of 80 km of SSMF in order to reach the normalized mean square error of less than 0.02 in relevance to the traditional split-step Fourier method. The OSNR thresholds are 19 dB and 21 dB, respectively, under scenarios of linear and nonlinear transmissions. Moreover, we verify that the OSNR threshold of accurate modeling is insensitive to both the modulation format and the RRC shaping of the input signal. Furthermore, we find that the cascaded use of cGAN well-trained for the single SSMF span is capable of modeling the multiple-span SSMF transmission in the case that the input OSNR threshold of 22.6 dB is satisfied. We believe that the identification of the OSNR threshold for data-driven optical fiber channel modeling is useful for the accurate and efficient emulation of long-haul fiber optical transmission.