This study evaluates the ability of Large Language Model (LLM)-based Subpopulation Representative Models (SRMs) to generalize from empirical data, utilizing in-context learning with data from the 2016 and 2020 American National Election Studies. We explore generalization across response variables and demographic subgroups. While conditioning with empirical data improves performance on the whole, the benefit of in-context learning varies considerably across demographics, sometimes hurting performance for one demographic while helping performance for others. The inequitable benefits of in-context learning for SRM present a challenge for practitioners implementing SRMs, and for decision-makers who might come to rely on them. Our work highlights a need for fine-grained benchmarks captured from diverse subpopulations that test not only fidelity but generalization.