A small diesel idles quite economically. Perhaps 0.1 g/hr. The extra power to turn the loaded alternator is also quite small. Gasoline engines running at reduced power are on the other hand quite inefficient. You'd have to do a careful test to be sure, but it isn't inconceivable that your diesel would burn less fuel than the Yamaha.

I went through this a long time ago when the Panda Fischer salesman was trying to sell me a $12,000 genset to save wear and tear on my $8000 main propulsion engine. It doesn't pencil out.

Of course, there a plenty of other considerations, for sure.

The main reason I would consider LiFePO4 batteries when I need to replace my AGMs is because the charge time is cut by a large percentage due to no tapering of the acceptance rate until full. Combine that with no urgent need to charge to any particular SOC and it changes the game. Those things are a lot more valuable on a boat than the weight savings or anything else associated with them.