For a higher density fuel, would that not spin the engine at the required RPM for a lower fuel volume? Take two theoretically identical engines and run them side by side. The FADEC will schedule whatever fuel flow it requires to meet the thrust or torque demand, and with a higher density fuel, this flow will be lower due to the higher density/BTU's in that quantity of fuel.
As for how it affects things, the higher the SG, the more weight you have in fuel, but the lower your cruise fuel flow will be, so taking it to the extreme, you could argue you need less fuel for that sector. Is it enough to ever make a difference?