The promise of passive seismology has increasingly been realized in recent years. Given the expense in installing and maintaining these seismic networks, it is important to extract as much information from the measurements as possible. In this context, the ellipticity or H/V amplitude ratio of Rayleigh waves can prove to be a valuable observable in ambient noise seismology due to its potential for constraining Vp structure, an advantage over group and phase-velocity dispersion, which are primarily sensitive to Vs. However, the suitability of the Rayleigh H/V ratio in noise-based studies depends on the accurate interpretation of measurements made on multi-component ambient-noise cross-correlations. We present a synthetic study that critically examines such measurements -- commonly interpreted in terms of the Rayleigh H/V ratio -- for realistic scenarios of spatially distributed and non-uniform noise sources. Using the Rayleigh-wave Green's function in a laterally homogeneous medium, we rigorously model multi-component cross-correlation for arbitrary noise-source distributions and extract from them standard estimates of the H/V ratio. Variation of these measurements with Vp is studied empirically by brute-force simulation. We find that the measurements depart significantly from the theoretical Rayleigh wave H/V for the medium in question, when noise sources are strongly directional or anisotropic. However, the sensitivity to Vp structure is comparable to that of the classic Rayleigh wave H/V. We also propose a new measurement for cross-correlations that has slightly greater sensitivity to Vp. Finally, uncertainty analysis on synthetic tests suggests that the ellipticity measurements can robustly resolve the Vp structure in the presence of noise (up to 10%). The primary utility of this method in scenarios when the noise level in the measured cross-correlations is significant (>~20%), is in being able to discern between different classes of models.