Conditional generative adversarial networks (cGANs) have enabled high-fidelity computational staining and destaining of hematoxylin and eosin (H&E) in digital pathology whole-slide images (WSI). However, their ability to generalize to out-of-distribution WSI across institutions without retraining remains insufficiently characterized. Previously developed cGAN models trained on 102 registered prostate core biopsy WSIs from Brigham and Women's Hospital were evaluated on 82 spatially unregistered WSIs acquired at Stanford University. To mitigate domain shift without retraining, a preprocessing pipeline consisting of histogram-based stain normalization for H&E-stained WSIs and channel-wise intensity calibration for unstained WSIs was developed. Because image registration was intentionally omitted for real-world deployment conditions, the reported quantitative results are conservative lower bounds reflecting both model performance and limited spatial alignment. Under these conditions, virtual destaining achieved a Pearson correlation coefficient (PCC) of 0.854, structural similarity index measure (SSIM) of 0.699, and peak signal-to-noise ratio (PSNR) of 18.41 dB. H&E restaining from computationally destained outputs outperformed direct staining from ground-truth unstained inputs across all metrics (PCC: 0.798 vs. 0.715; SSIM: 0.756 vs. 0.718; PSNR: 20.08 vs. 18.51 dB), suggesting that preprocessing quality may be more limiting than model capacity. Qualitative pathological review indicated preservation of benign glandular structures while showing that malignant glands were often rendered with vessel-like morphologies. These findings support the feasibility of applying cGAN-based computational H&E staining and destaining generative models to external WSI datasets using preprocessing-based adaptation alone while defining specific morphological targets for future domain adaptation.