Spatial and intensity normalization are nowadays a prerequisite for neuroimaging analysis. Influenced by voxel-wise and other univariate comparisons, where these corrections are key, they are commonly applied to any type of analysis and imaging modalities. Nuclear imaging modalities such as PET-FDG or FP-CIT SPECT, a common modality used in Parkinson's Disease diagnosis, are especially dependent on intensity normalization. However, these steps are computationally expensive and furthermore, they may introduce deformations in the images, altering the information contained in them. Convolutional Neural Networks (CNNs), for their part, introduce position invariance to pattern recognition, and have been proven to classify objects regardless of their orientation, size, angle, etc. Therefore, a question arises: how well can CNNs account for spatial and intensity differences when analysing nuclear brain imaging? Are spatial and intensity normalization still needed? To answer this question, we have trained four different CNN models based on well-established architectures, using or not different spatial and intensity normalization preprocessing. The results show that a sufficiently complex model such as our three-dimensional version of the ALEXNET can effectively account for spatial differences, achieving a diagnosis accuracy of 94.1% with an area under the ROC curve of 0.984. The visualization of the differences via saliency maps shows that these models are correctly finding patterns that match those found in the literature, without the need of applying any complex spatial normalization procedure. However, the intensity normalization -- and its type -- is revealed as very influential in the results and accuracy of the trained model, and therefore must be well accounted.