Graph convolutional networks (GCN) leverage topology-driven graph convolutional operations to combine information across the graph for inference tasks. In our recent work, we have studied GCNs with covariance matrices as graphs in the form of coVariance neural networks (VNNs) that draw similarities with traditional PCA-driven data analysis approaches while offering significant advantages over them. In this paper, we first focus on theoretically characterizing the transferability of VNNs. The notion of transferability is motivated from the intuitive expectation that learning models could generalize to "compatible" datasets (possibly of different dimensionalities) with minimal effort. VNNs inherit the scale-free data processing architecture from GCNs and here, we show that VNNs exhibit transferability of performance over datasets whose covariance matrices converge to a limit object. Multi-scale neuroimaging datasets enable the study of the brain at multiple scales and hence, can validate the theoretical results on the transferability of VNNs. To gauge the advantages offered by VNNs in neuroimaging data analysis, we focus on the task of "brain age" prediction using cortical thickness features. In clinical neuroscience, there has been an increased interest in machine learning algorithms which provide estimates of "brain age" that deviate from chronological age. We leverage the architecture of VNNs to extend beyond the coarse metric of brain age gap in Alzheimer's disease (AD) and make two important observations: (i) VNNs can assign anatomical interpretability to elevated brain age gap in AD, and (ii) the interpretability offered by VNNs is contingent on their ability to exploit specific principal components of the anatomical covariance matrix. We further leverage the transferability of VNNs to cross validate the above observations across different datasets.