The NamUs database does show that there was DNA tests done on the fetus. Look in the DNA section and it lists an ID number for the fetus.
https://identifyus.org/cases/8913
As for the father ever being in trouble, I don't think that LE routinely take DNA on everybody arrested, just if they are suspected of a crime that would involve DNA (rape, murder, etc.) I am pretty sure that they were not using DNA tests in the late 1970's.
Changing the subject: This is the first that I have come across this case. I grew up in NJ less than an hour from where Beth Doe was found. I graduated high school in 1977, so we would be close to the same age. Something about her image is eerily familiar. I can't place it, but it could be a childhood memory of a girl that was in the foster care system. I can't remember her name but I think it started with a D - Darlene, Donna or Debbie? She was in our school district for maybe a year or two, probably around 1972/1973. I remember the place where she lived, it was a sort of group home or home for "wayward girls" as my mother described it. It seems to me that she was of Italian descent, which would match the Mediterranean mentioned.
Another thought is that she could have been part of culture that practiced arranged marriages when the girls were in their mid-teens. One of my high school friends was from Greece and her family arranged to have her husband brought over when she was 16. She was pregnant by the time she was 17 and by the time she was 20 she was divorced. The guy had beat her pretty badly but still she was shunned from the family when she left him. Beth Doe's murder seems very personal, not just random. So could it be that she was pregnant when the man she was promised to came to the US and when he found out, he killed her? Just a thought...