Convolutional neural networks (CNN) have established state-of-the-art performance in computer vision tasks such as object detection and segmentation. One of the major remaining challenge concerns their ability to capture consistent spatial attributes, especially in medical image segmentation. A way to address this issue is through integrating localization prior into system architecture. The CoordConv layers are extensions of convolutional neural network wherein convolution is conditioned on spatial coordinates. This paper investigates CoordConv as a proficient substitute to convolutional layers for organ segmentation in both fully and weakly supervised settings. Experiments are conducted on two public datasets, SegTHOR, which focuses on the segmentation of thoracic organs at risk in computed tomography (CT) images, and ACDC, which addresses ventricular endocardium segmentation of the heart in MR images. We show that if CoordConv does not significantly increase the accuracy with respect to standard convolution, it may interestingly increase model convergence at almost no additional computational cost.