The vision of a "virtual cell" - a computational model that simulates biological function across modalities and scales - has become a defining goal in computational biology. While powerful unimodal foundation models exist, the lack of large-scale paired data prohibits the joint training of multimodal approaches. This scarcity favors compositional foundation models (CFMs): architectures that fuse frozen unimodal experts via a learned interface. However, it remains unclear when this multimodal fusion adds task-relevant information beyond the strongest unimodal representation and when it merely aggregates redundant signal. Here, we introduce the Synergistic Information Score (SIS), a metric grounded in partial information decomposition (PID), that quantifies the information gain achievable only through cross-modal interactions. Extending theoretical results from self-supervised learning, we show that standard alignment-based fusion objectives on frozen encoders inherently collapse to detecting linear redundancies, limiting their ability to capture nonlinear synergistic states. This distinction is directly relevant for tasks aiming to link tissue morphology and gene expression. Benchmarking ten fusion methods on spatial transcriptomics datasets, we use SIS to demonstrate that tasks dominated by linear redundancies are sufficiently served by unimodal baselines, whereas complex niche definitions benefit from synergy-aware integration objectives that enable cross-modal interactions beyond linear alignment. Finally, we perform a scaling analysis which highlights that fine-tuning a dominant unimodal expert is the most sample-efficient path for standard tasks, suggesting that the benefits of multimodal frameworks only emerge when tasks depend on information distributed across mod