A city on a single land tile with no other land in range would only be able to build districts that go in the water (Harbor being the only one we know of), and so there would be a number of problems. It would be unable to construct any buildings that require any land districts other than the city center. It would also have a Population Housing problem, since it won't be able to construct improvements that provide housing (Farms, Plantations, Neighborhoods). So unless there are a lot more buildings that can be built in the city center (which seems unlikely), and unless there are water-based improvements that provide housing (which seems unlikely), a single-tile island city will have only the most basic buildings (monument, granary, walls, lighthouse, docks), and won't be able to increase the population beyond what the city center can support (which looks in the early gameplay video to be about 7).