I know in the Canterbury Tales one of the stories is about a rather ungodly Friar. I've also seen illuminated manuscripts of monks performing less than holy acts.
I can only speak for the middle ages proper, which is basically the biggest chunk in the middle of the years you mention. When considering the middle ages, it's basically wrong to think of anyone as not being a Christian (edit: aside from Jews, who were problematic and often not considered). There were certainly Christians who cleaved more or less strongly to the Church's doctrines, even to the extent of widespread popular heresies such as Catharism or Lollardy, but the category we think of Atheism today did not exist, and if you asked those Cathars what religion they were, they would still have said Christian (if they understood the question at all, which they wouldn't, because the idea of different religions is one that has evolved a lot over the centuries).
Now, I'm not saying Christians didn't have doubts; monks are often surprisingly frank about admitting they are unsure. Henry of Huntingdon, an English historian from the 12th century, writes about his decision to include miracles despite his doubts as to their reality. However, that's a question of doubting things like miracles done today. There is also some evidence to suggest that less learned people were known to question transubstantiation, as many books of examples for priests to use in sermons contain stories about doubters of the Eucharist experiencing some miracle and repenting. However, the idea of someone evaluating the costs and benefits of becoming a monk, and deciding that the scholarship is "worth" all the religion is quite anachronistic, and also misunderstands the processes involved in becoming a monk (which I am by no means an expert in, but understand to occur usually at a relatively young age). Hope that helps, and sorry to disappoint. If you've got any follow up questions, please send them my way and I'll do my best to answer them!