The human Y is a genetically degenerate chromosome, which has lost about 97% of the genes originally present. Most of the remaining human Y genes are in large duplicated segments (ampliconic regions) undergoing intense Y-Y gene conversion. It has been suggested that Y-Y gene conversion may help these genes getting rid of deleterious mutations that would inactivate them otherwise. Here, we tested this idea by simulating the evolution of degenerating Y chromosomes with or without gene conversion using the most up-to-date population genetics parameters for humans. We followed the fate of a variant with Y-Y gene conversion in a population of Y chromosomes where Y-Y gene conversion is originally absent. We found that this variant gets fixed more frequently than the neutral expectation, which supports the idea that gene conversion is beneficial for a degenerating Y chromosome. Interestingly, a very high rate of gene conversion is needed for an effect of gene conversion to be observed. This suggests that high levels of Y-Y gene conversion observed in humans may have been selected to oppose the Y degeneration. We also studied with a similar approach the evolution of ampliconic regions on the Y chromosomes and found that the fixation of many copies at once is unlikely, which suggest these regions probably evolved gradually unless selection for increased dosage favored large-scale duplication events. Exploring the parameter space showed that Y-Y gene conversion may be beneficial in most mammalian species, which is consistent with recent data in chimpanzees and mice.