General-purpose audio representations aim to map acoustically variable instances of the same event to nearby points, resolving content identity in a zero-shot setting. Unlike supervised classification benchmarks that measure adaptability via parameter updates, we introduce VocSim, a training-free benchmark probing the intrinsic geometric alignment of frozen embeddings, with no parameters updated and no labels used (a label-free PCA whitening is fit per subset to correct anisotropy). VocSim aggregates 125k single-source clips from 19 corpora spanning human speech, animal vocalizations, and environmental sounds, isolating content representation from source separation (polyphonic mixtures are out of scope). We evaluate embeddings with Precision@k for local purity and the Global Separation Rate (GSR) for point-wise class separation, calibrated by lift over an empirical permutation baseline. A simple pipeline of frozen Whisper features, time-frequency pooling, and label-free PCA yields strong zero-shot performance with stable GSR rankings across domains (Kendall's tau = 0.60). However, on blind low-resource speech (Shipibo-Conibo, Chintang), local retrieval collapses while remaining above chance, exposing a cross-lingual speech generalization gap. As external validation, our top embeddings predict avian perceptual similarity, improve bioacoustic classification, and achieve state-of-the-art on the HEAR benchmark. We release data, code, and a public leaderboard.