I would start with that repair first IMO but youll have to remove the carb, then pull off the float bowl youll see the float and then the jet dead center that you can remove with a flat head screw driver. Remove that then clean out the port really well but dont OVERSIZE it by removing material as its brass.
@MRWood also make sure to buy the rebuild kit for the carb so you have all the gaskets and seals needed when you tear it down, so you dont end up with leaks.
https://www.crowleymarine.com/yamaha/oem-parts/outboard/2004/f9-9mshc/carburetor?ref=8 - use that diagram for reference