Method: ProRSeg was trained using 5-fold cross-validation with 110 T2-weighted MRI acquired at 5 treatment fractions from 10 different patients, taking care that same patient scans were not placed in training and testing folds. Segmentation accuracy was measured using Dice similarity coefficient (DSC) and Hausdorff distance at 95th percentile (HD95). Registration consistency was measured using coefficient of variation (CV) in displacement of OARs. Ablation tests and accuracy comparisons against multiple methods were done. Finally, applicability of ProRSeg to segment cone-beam CT (CBCT) scans was evaluated on 80 scans using 5-fold cross-validation. Results: ProRSeg processed 3D volumes (128 $\times$ 192 $\times$ 128) in 3 secs on a NVIDIA Tesla V100 GPU. It's segmentations were significantly more accurate ($p<0.001$) than compared methods, achieving a DSC of 0.94 $\pm$0.02 for liver, 0.88$\pm$0.04 for large bowel, 0.78$\pm$0.03 for small bowel and 0.82$\pm$0.04 for stomach-duodenum from MRI. ProRSeg achieved a DSC of 0.72$\pm$0.01 for small bowel and 0.76$\pm$0.03 for stomach-duodenum from CBCT. ProRSeg registrations resulted in the lowest CV in displacement (stomach-duodenum $CV_{x}$: 0.75\%, $CV_{y}$: 0.73\%, and $CV_{z}$: 0.81\%; small bowel $CV_{x}$: 0.80\%, $CV_{y}$: 0.80\%, and $CV_{z}$: 0.68\%; large bowel $CV_{x}$: 0.71\%, $CV_{y}$ : 0.81\%, and $CV_{z}$: 0.75\%). ProRSeg based dose accumulation accounting for intra-fraction (pre-treatment to post-treatment MRI scan) and inter-fraction motion showed that the organ dose constraints were violated in 4 patients for stomach-duodenum and for 3 patients for small bowel. Study limitations include lack of independent testing and ground truth phantom datasets to measure dose accumulation accuracy.