Visual place classification from a first-person-view monocular RGB image is a fundamental problem in long-term robot navigation. A difficulty arises from the fact that RGB image classifiers are often vulnerable to spatial and appearance changes and degrade due to domain shifts, such as seasonal, weather, and lighting differences. To address this issue, multi-sensor fusion approaches combining RGB and depth (D) (e.g., LIDAR, radar, stereo) have gained popularity in recent years. Inspired by these efforts in multimodal RGB-D fusion, we explore the use of pseudo-depth measurements from recently-developed techniques of ``domain invariant" monocular depth estimation as an additional pseudo depth modality, by reformulating the single-modal RGB image classification task as a pseudo multi-modal RGB-D classification problem. Specifically, a practical, fully self-supervised framework for training, appropriately processing, fusing, and classifying these two modalities, RGB and pseudo-D, is described. Experiments on challenging cross-domain scenarios using public NCLT datasets validate effectiveness of the proposed framework.