Was it even possible or legal in in the deep South of the 1850's?
Yes, this was true. While miscegenation was illegal in many states, it was not illegal in Louisiana. So Mistress Shaw was a real person mentioned in the book. Even the part about Patsey getting soap from her was true. Not only that, but Mr. Bass, played by Brad Pitt in the movie, lived with a black woman, too. They weren't married, but Bass had left a wife back in Canada so he couldn't marry. AND the slave trader, played by Paul Giamatti in the movie, was living with a black woman, too. And then there was also the case in the movie of Eliza, who ends up in the slave prison with Northup and her 2 children--she lived as mistress with a white man though they were not married and she was still a slave. They had their own house together. But that was in Virginia, where the law was different. And it was also true, as in the movie, that when he was out one day, his grown daughter sold Eliza and her 2 children down the river.
In the majority of states, miscegenation was illegal until the 20th century, so it wouldn't have been legal.
However, there are plenty of accounts of slave owners using their slaves for sex, often resulting in children.
And one more example: Thomas Jefferson had a nephew who lived as husband and wife with a former slave. I don't know if they were legally married, though.