did [Nazi Germany] have romance novels?

What a great question! I went to wikipedia which paraphrased a great quote from NYT

Germans love erotic romance...The company publishes German writers under American pseudonyms "because you can't sell romance here with an author with a German name"

which suggests that they are a recent development. Maybe there was a huge market for Georgette Heyer, but little production in Germany.

One thing that is great about wikipedia is the link to corresponding articles in other languages. "Romance Novel" in English links to an article entitled "Love- and Family-Novels." That suggests that the genres were different, at least at some point in time. That article mentions Hedwig Courths-Mahler as a prolific author who was a supporter of the SS and I think registered for censorship. But she rejected the specific censorship, so she published nothing after 1935 and her old books gradually fell out of print. But I'm not sure she really was a romance author, because of the discrepancy of genres.