In addition to dieselization, an interesting naval propulsion what-if is drastically more powerful boilers. In particular, in 1933 the RN tried a Velox boiler from the Swiss BBC for a destroyer, promising an order of magnitude improvement in steam generation per floor area. Despite this test, at around the same time the RN decided to standardize on the Admiralty pattern boiler, so nothing came of it. But what if they had gone down that path?
And how did the Velox boiler achieve such power density? Well, BBC had the idea to compress the incoming air (=more heat generation per volume), and increase the velocity of the flue gasses. Ok, so add a compressor to compress the incoming air. And how to drive the compressor? Well, there's quite a lot of energy in those flue gasses, so what about a (drumroll..) turbine wheel? I guess you can see where this is going. Now with the technology of the day there wasn't much excess power available after running the compressor (presumably required a lot of extra air to avoid melting the turbine blades with the available alloys, inefficient blade design etc.), so it was clearly a boiler and not a gas turbine engine.
But if one of the big navies had gone for this system in the early thirties and shoveled R&D money into it, we could have had gas turbines a few years sooner, with interesting ramifications both for WWII naval ships as well as aircraft.