Multimodal Large Language Models (MLLMs) have recently been explored as face verification systems that determine whether two face images are of the same person. Unlike dedicated face recognition systems, MLLMs approach this task through visual prompting and rely on general visual and reasoning abilities. However, the demographic fairness of these models remains largely unexplored. In this paper, we present a benchmarking study that evaluates nine open-source MLLMs from six model families, ranging from 2B to 8B parameters, on the IJB-C and RFW face verification protocols across four ethnicity groups and two gender groups. We measure verification accuracy with the Equal Error Rate and True Match Rate at multiple operating points per demographic group, and we quantify demographic disparity with four FMR-based fairness metrics. Our results show that FaceLLM-8B, the only face-specialised model in our study, substantially outperforms general-purpose MLLMs on both benchmarks. The bias patterns we observe differ from those commonly reported for traditional face recognition, with different groups being most affected depending on the benchmark and the model. We also note that the most accurate models are not necessarily the fairest and that models with poor overall accuracy can appear fair simply because they produce uniformly high error rates across all demographic groups.