Biases have marked medical history, leading to unequal care affecting marginalised groups. The patterns of missingness in observational data often reflect these group discrepancies, but the algorithmic fairness implications of group-specific missingness are not well understood. Despite its potential impact, imputation is too often an overlooked preprocessing step. When explicitly considered, attention is placed on overall performance, ignoring how this preprocessing can reinforce groupspecific inequities. Our work questions this choice by studying how imputation affects downstream algorithmic fairness. First, we provide a structured view of the relationship between clinical presence mechanisms and groupspecific missingness patterns. Then, through simulations and real-world experiments, we demonstrate that the imputation choice influences marginalised group performance and that no imputation strategy consistently reduces disparities. Importantly, our results show that current practices may endanger health equity as similarly performing imputation strategies at the population level can affect marginalised groups differently. Finally, we propose recommendations for mitigating inequities that may stem from a neglected step of the machine learning pipeline.