The Einei Shmuel writes that "Lav ba'Shamayim Hee" and "Ein Mashgichin b'Bas Kol" only apply to cases of Halachah. This means that the question cannot be directly answered by a Bas Kol. However, if there is merely an uncertainty regarding who is the father of a child, the question can be decided by a Bas Kol or the Manna, despite the fact that this will have Halachic ramifications (see also Kapos Temarim who deals with this topic at length).

All the best,

Yaakov Montrose