I can't insert the quote, but you didn't believe they would overturn Roe back in 2016. Don't put anything past these people. Alito has essentially declared that he wants to get rid of Obergfell. I doubt he'd get much resistance from the rest of the right wing justices. After that it's contraception, then Lawrence, then Loving.
As you have said here, overturning Loving would likely have little impact, because virtually no lawmakers would make IR marriage illegal, and I doubt LEOs would enforce it. There are likely old laws on the books in the south, though.