@Rob --
Regardless of what the offspring would think there would be no reason to attach any supernatural claims to such a birth as science is well prepared to explain it. Such a child would be female and apparently the result of the only recorded natural instance of human parthenogenesis, which is very likely what the OB/GYN would tell the expectant mother.
If I found out that I didn't have a biological father I would, indeed, be quite confused(infinitely more confused as I'm male, and thus human parthenogenesis would be out of the question as an explanation) but I still wouldn't go jumping the gun and saying that I was the son of a god(or the god), that takes a hell of a lot of arrogance and I'm just not capable of that much arrogance.