Republic titles don't require the holder to be landed, only a patrician family. He will hold the title until he dies and then it will be destroyed. This also occurs with non-titular Republic titles such as Genoa or Venice. These titles are the same as the Duchy (or Kingdom in the case of Venice) titles so they can be usurped. A titular republic title can't be held by a feudal lord, so you won't be able to usurp it. You can hold the Duchy of Lukania/Salerno of which the county of Amalfi is de Jure.
This sounds like the most likely scenario. As republics doesn't have to be landed, since they technically got all the "Houses" as vassal titles. I'll double check it with the team just in case. But it sounds like it would be WAD.