Yes I know the battery would drain quickly...
But the time spent accelerating is minimal compared to the time spent coasting
And yes a transmition between the motor would probably be needed
(there would be energy lossed here, but mixed with 98% Effiecient motors it wouldn't be all lost
http://www.tip.csiro.au/Machines/success/sc.html , a benefit to this motor is that it is flat and lightweight compared to traditional motors)
I work around mills that consistently operate at 10k plus rpm they are extremely reliable, yes I agree a 100x gear ratio is high, but it is doable. Besides the turbine itself would be more complicated and expensive to machine.
That and your either forgetting or just leaving out the fact that tremendous power can be captured from the aft end of the turbo charger. Dont forget that end also spins in the 100k rpm range, such power would most likely require a very large capacitor rather then a battery.
Also in the decelerating corner of things... you spend just as little time decelerating as you do accelerating
And who knows If you have the money why not invest in a regenerative braking system... that goes straight to the capacitor