I sometimes hear that there were a number of factors that conspired to degrade the reputation of the Catholic Church in large parts of Europe in the lead up to the reformation, commonly cited is the humiliating Avignon papacy and especially the Western Schism that came from it, a degradation in Church standards and discipline, but also the idea that the outbreak of the plague and its recurrent appearance over the centuries caused a loss of faith in the Church. The argument usually goes that clergy were in a bit of a Catch 22 situation, a lot of them stayed with their sick parishioners and tried to help them, but that meant that priests could be particularly vulnerable to catching the disease and dying, which would make it seem like the church did not have god's favour to allow churchmen to survive the catastrophe and were being punished as much if not more harshly than the rest of the population. Alternatively some clergy didn't have the stomach to stay in a place that they knew was being ravaged by the disease, causing them to avoid contact with their flock or even flee, which could build up resentment that many in the church were abandoning their responsibilities in a time of disaster, both situations being a bad outcome for people's opinion that the church still held god's favour.
Additionally, other arguments are that just generally the difficulty in creating a coherent, useful strategy to deal with such a disaster damaged people's faith that the Church was able to help in a serious way, as well as increasingly heavy handed actions by temporal authorities to enforce quarantines that increased their own power relative to the church (I'll admit this one confuses me since I though that quarantines were something that had a lot of Church involvement, but then I also understand that quarantines could exceptionally controversial in application and that a lot of people simply didn't, and don't, fully appreciate their importance). Finally that, in the midst of the disaster, spontaneous grassroots movements like the Flagellants started to spring up, often quite explicitly against the wishes of the Catholic hierarchy, that started to create a tradition of popular religious movements without church approval.
I don't know if this is really true, but I would be curious if the Black Death helped set in motion some of the events that helped lead to the Reformation.
Basically: no.
Most people's idea of the 15th century is essentially: the Battle of Agincourt, Joan of Arc, the fall of Constantinople to the Ottomans, and the War of the Roses. (Also Columbus, but people don't tend to associate that with the 15C). If there's something about religion tucked in there, it's that Jan Hus was a heretic and the Church burned him at the stake.
In fact, the 15th century has been called "the most ecclesiastically devout in the Middle Ages." Not just the most religious. The era when people expressed their religious beliefs, in thought and in deed, more strongly and more strongly through the Church than ever before.
Oh, and it was a German scholar, studying the German cities who led the way in the Reformation, who first made this observation.
My favorite example comes from Kraftshof, which lay close to the Reformation-pioneering city of Nuremberg. In 1402, villagers from Kraftshof and six nearby villages pooled their money to provide a house and salary for a dedicated priest at the Kraftshof church (previously served only occasionally). They petitioned the bishop for a priest who could say Mass for them every day, to give them spiritual nourishment before each day's labor.
Thirty years later, they wrote to the bishop again. They weren't satisfied with just some daily Mass. They wanted someone who could preach them actual sermons, for religious instruction...and perhaps more to the point, who could actually preach those sermons well. The Kraftshof villagers, and their neighbors, wanted the rituals of the Church and the lessons promoted by the Church. And they were willing to pay quite a large amount of money for it.
You can point to countless other examples. In 1215, the Fourth Lateran Council had decreed that all Christians of both sexes must receive the Eucharist once a year, at Easter, preceded by saying confession to their parish priest and receiving absolution for their sins. Well, it was only in the 1400s that this was pretty much accomplished throughout Latin Europe. And accomplished with vigor: lay people fought for, and eventually received, the right to choose their own priest to confess to--and evidence suggests at least some of them sought out the strictest ones they could find. By the latter half of the century, dioceses were instituting rules for churches to offer multiple confession opportunities per year (revolutionary).
Heck, you can even take indulgences, the thing that so steamed Luther. Indulgences were an age-old belief in Christianity. But the fad for them that the Augustinian friar would rage against really only got going in the 1470s. And even then, a large portion of indulgence certificates were counterfeit--not officially sanctioned by the Church. They existed because lay people wanted them.
There's so much else that can be said. Bubonic plague kept coming back throughout the rest of the 14th and 15th centuries (and down to the early 20th, for what it's worth...). But each time, it got more localized, and less deadly, and less fearsome. Flagellants predated the Black Death, and they were SO much not the first lay-founded religious movement.
I suppose that in the sense of "everything contributes to everything that follows it," the Black Death led to the Reformation. But in practice, there were 1 3/4 centuries between the arrival of pestilence and the Diet of Worms. And for western Christians and the western Church alike, those 170 years were some of the most religiously healthy of all time.