I have fitted a lightened flywheel to my Westfield so have some "before and after" experience on the matter, albeit not on an Omega.
IIRC, I started off with about 18 Kg of flywheel and ended up with 5.5. On a 600Kg car that's a worthwhile weight reduction in itself. Not on a 1700Kg car though.
There is less energy used in spinning-up the flywheel as you accelerate, of course, but probably no more than a couple of horsepower even in first gear, and the rate of change of RPM is so slow in the higher gears it really is irrelevant. I certainly noticed no increase in in-gear acceleration.
The main (probably only) benefit is that when changing up the engine revs decay quicker meaning that you can grab the next gear quicker and without a load of stored momentum in the flywheel being unleashed suddenly when you drop the clutch and causing you to break traction. This is an observation based on an engine that redlines at 7400. Not sure it would be as valid on a lower-revving V6, which has more inertia anyway, regardless of the flywheel.
The other thing to consider is that less flywheel will make the car more prone to stalling when pulling away and during urban driving, something that will be worse with a heavier car, of course.
Personally, it wouldn't be that high up my Omega tuning wish-list.
Kevin