Now this is a bit complicated.
I personally don't believe that we should believe in every myth.After all, nothing would stop prople from making up stories.I mean, see nowadays.The gods were named demons from the christians.Nothing put them back in their place.
Then, we don't know if the gods and goddesses are embodied or not.But then there is the concept of astral birth.
At the other hand, there are the godspouses.They are under great skepticism, but they claim to have love relationships with the divines.Well, who knows...
My opinion is that yes, they could have offspring with humans nowadays, but they don't, either because some of them personally don't like the idea, or because the conditions may be harder nowadays.