Sensor self-noise is an important aspect in the design of spherical microphone arrays. We consider the application of binaural rendering of spherical microphone array signals in this paper. We use the Real-Time Spherical Array Renderer (ReTiSAR) to analyze the frequency-dependent white-noise-gain i.e., the improvement of the signal-to-noise ratio (SNR) between a selected microphone of the array and the binaural output signals. The configuration of the array as well as of the processing pipeline have been shown to strongly influence the spectral properties and the overall level of the noise in the binaural signals. We found that arrays with small radii reduce the SNR by approximately 8 dB unless a strong limitation of the radial filter gain is applied. Some array configurations with larger radii and number of microphones (above spherical harmonics order 4) are capable of increasing the SNR in the rendered signals by up to 9 dB. We also found variations in the spectral properties of the rendered self-noise as a function of the head orientation for higher-order Lebedev grids.