Somewhere in her twenty-four episode lecture series on Greek myth, Elizabeth Vandiver takes up this idea. She asserts that no one could successfully try to explain away a pregnancy by saying she had been knocked up by a god. Vandiver explains that these sorts of incidents were believed to have occurred 'way back then' and were not something that unfolded in real time in current society.

In general, I agree with her. Even in societies with active beliefs in sexually-aggressive forest entities, for example, one would have a hard time convincing the village that a pregnancy was the result of a supernatural relationship. We can ponder whether Mary ever really asserted that Jesus was born as a result of a supernatural liaison: oral tradition often gives culture heroes extraordinary births and folklore can form around these sorts of people very quickly (people were telling stories about George Washington's youth very soon after he passed from the scene).

In general, while people believe in stories of extraordinary conception and birth, they generally project them backwards to a former time and are less likely to embrace that sort of explanation for a woman who finds herself pregnant in a current situation.