There are not currently plans for such a test. However, the Boe-CFT Crewed Flight Test has experienced problems, and there is speculation about another test flight before the first operational flight Starliner-1. Will such a flight happen?
When I wrote the question I didn't really think about that possibility; I was basically assuming it would be called another flight test mission. I think the best interpretation is that if it's called a test mission, this resolves positively. If it's called Starliner-1, and labeled as an operational mission, it resolves negatively (whether crewed or otherwise). (Noting that another "test" mission could also be a crewed mission, just as CFT-1 is a crewed test mission.) So the weird edge case is something named an "operational" mission, but not "Starliner-1". I'm inclined to think this should resolve No in that case (it's not "another test flight before the first ..."), but I could see a case for "it's a test even if they're not calling it that". I think it's simplest not to second-guess what counts as a test mission.
I suppose one could write a question for "will there be an uncrewed Starliner flight before the next crewed flight" or similar, if you thought the possibility was likely.