As a person trying to pursue historical work, that is something beyond what I can investigate. The answer is obviously no. Ancient, medieval, early Christians never had such a thing. Therefore, the historical quest for the historical Jesus is not essential for simple, authentic Christian faith. Even today in the Third World there are all sorts of uneducated, illiterate peasants who would not know a word about historical Jesus, theology or anything else, who I'm sure have a very strong, authentic Christian faith and maybe much better than mine.
Theology never floats outside history.
It's not very surprising, therefore, that Reimarus's quest during the Enlightenment looks rather different from Schleiermacher's quest during German romanticism, looks rather different from Bultmann's quest during the heyday of existentialism in Germany. Hence if Christians today wish to articulate their faith in Jesus Christ in a fashion that reflects and speaks to the culture they live in, there has to be some awareness of historical critical consciousness. The patristic and medieval periods did not have that concern. You notice that doesn't hold true so much for the basic affirmations of faith. That's the importance of certain basic credal affirmations that try to remain as fundamental, as unspeculative and undeveloped as possible.