If you're talking about the little chrome screw for idle mixture, it probably won't make much difference. All engines have a fuel consumption curve that starts a bit high when they are new, goes a little lower as they are broken in, flattens out over most of the life of the engine and then goes high again when the engine is well worn. For that engine, the difference in actual gallons consumed would be very small and almost non-discernible without some sophisticated test equipment. In other words, you probably won't notice.
Not sure if we've covered this ground before but are you routinely draining the carb bowl and item #2 in the link below?
http://www.boats.net/parts/search/Honda/Outboard Engine/2006/BF15D6 LRA /FUEL PUMP/parts.html