Despite current advancement in the field of biomedical image processing, propelled by the deep learning revolution, multimodal image registration, due to its several challenges, is still often performed manually by specialists. The recent success of image-to-image (I2I) translation in computer vision applications and its growing use in biomedical areas provide a tempting possibility of transforming the multimodal registration problem into a, potentially easier, monomodal one. We conduct an empirical study of the applicability of modern I2I translation methods for the task of rigid registration of multimodal biomedical and medical 2D and 3D images. We compare the performance of four Generative Adversarial Network (GAN)-based I2I translation methods and one contrastive representation learning method, subsequently combined with two representative monomodal registration methods, to judge the effectiveness of modality translation for multimodal image registration. We evaluate these method combinations on four publicly available multimodal (2D and 3D) datasets and compare with the performance of registration achieved by several well-known approaches acting directly on multimodal image data. Our results suggest that, although I2I translation may be helpful when the modalities to register are clearly correlated, registration of modalities which express distinctly different properties of the sample are not well handled by the I2I translation approach. The evaluated representation learning method, which aims to find abstract image-like representations of the information shared between the modalities, manages better, and so does the Mutual Information maximisation approach, acting directly on the original multimodal images. We share our complete experimental setup as open-source (https://github.com/MIDA-group/MultiRegEval), including method implementations, evaluation code, and all datasets, for further reproducing and benchmarking.