I don't normally come in this section, but...
...seeing a number of people who would not normally post in an RX-8 section...
It *IS* possible for a lightened flywheel to affect idle...
It is even possible that it could be so light that engine will not be able to run a stable idle.
The flywheel is...a flywheel.
http://en.wikipedia.org/wiki/Flywheel
It stores potential energy, which is definied by it's mass.
Larger the mass -> larger the potential energy stored.
By lowering the mass, the flywheel cannot store as much potential energy now.
Think of it as a "buffer" for the mechanical energy by the engine.
The engine does not produce a steady-state amount of energy at any one time.
Due to it's configuration and design, it's a complex bunch of harmonics of bursts of energy.
This is where a "heavy" flywheel can help.
The old-school guys who used to run insanely light flywheels can atest that these can affect idle like mad.
Couple super lightened flywheels with unsteady idles due to massive porting - i.e. bridges and peripherals - you got one ungodly engine trying to idle properly.
This is why these things do no idle below 1,500RPM's and in some cases up to 2,000RPM's!
-Ted