I cannot contradict individual cases, but among the population as a whole, it is not seen in the data. The vast majority of users give up within just a few days or weeks, so users who leave because of downvotes would likely be a small minority among the noise of others leaving for reasons that they face more immediately after joining.
I also have not examined the effect on power downs or the Hive price, perhaps the harms of downvotes could show up there instead.