I know that there was a period where celibacy was not really a trend in the catholic church, so I am asking more about the actual period where it was expected to remain celibate.
The reason I ask is because the very idea kind of disturbs me that monks or those involved in the Church did not pass on their genes. It would be like as if today all scientists and academics from Harvard, Stanford, MIT etc. could not have children thus reducing those smart genes over time.
Well, at the very least in Italy, we know for a fact that some priests (and other men of the cloth) indeed had sex, had mistresses, and ultimately fathered children. We know this, because inquisitorial documents describe a) priests who were discovered to have broken their celibacy and b) women who atempted love magic (or hired mages to perform it for them) in the hopes that it would make their clerical boyfriends faithfull to them. Much of this was, eventually, stopped by the counter reformation though.
I have not encountered sources that show this happening in the rest of europe, but I find it likely that the italiens were not any more "deviant" anyone else. So some genes were in fact passed on - but since their offspring rarely were officially recognized by their fathers, I doubt it did them much good.
Sources: O’Neil, Mary. “Magical Healing, Love Magic and the Inquisition in Late Sixteenth-century Modena”, i Inquisition and Soceity in Early Modern Europe. Haliczer, Stephen (ed).
Also inquisitorial sources from the Italian town of Orbetello - according to Louise Nyholm Kallestrup.