I would answer quoting Anselm of Canterbury, who stated “credo ut intelligam, intelligo ut credam”, namely “I believe in order to understand, I understand in order to believe”. The latter part corresponds to what the students labelled as the role of reason in theology, namely the need to continue improving one’s understanding of theological truths in order to deepen one’s faith in them. The first part is an answer to the student’s query about the role of faith.
In other words, unless one had faith in, say, the real presence of Śrī Viṣṇu in a given idol, one would not start elaborating a theory about the arcāvatāra. In a Catholic milieu, one might think at Antoine Arnauld’s discussion of the signification of demonstrative pronouns inspired by his faith in the transubstantiation during the Mess (in his L’Art de penser).

Long story short:
1. Faith, I think, can motivate one to look at a topic one would have not thought of.
2. Moreover, it can help one overcome one’s initial disbelief and think more thoroughly about a topic.

This should not be confused, however, with the case of stiffening in a position without accepting to discuss counter-positions. Faith can promote philosophy if it is so self-confident to be able to lead to an open-minded intellectual journey.

What do readers think? Can faith help philosophical enterprises?