for example a twin turbo engine on 100oct gas makes 1100HP and the same engine on 91 pump gas makes roughly 850 HP.... would an alky injection kit give me the same results using 91 oct as it would using 100 oct?

 

No......But it will be close.

Water does not burn. Air and fuel , does. Adding water to the combustion process cools and moderates peak combustion temps, supressing detonation allowing more boost and ignition timing than without, but water displaces air and fuel that could have been making power.
(Reduces volumetric efficientcy.)

When water turns to steam it does help push the piston down, some. But over all a motor that runs on high boost and high octane gas will make more power than a motor that relies on water injection to alow high boost without detonation. Mixing water with alchol helps the net volumetric efficiently. Best mix for power is about 45 to 55 % water/ methanol.

The beauty of water injection is it allows high(er) boost without detontation using cheaper street pump gas, with very near the same power and as good reliability, but at less cost.

Water can make up , up to 1/3 the total fuel/water volume entering the engine. Becuase of this the amount of actual fuel burned to produce the power is 1/3 less. Less cost.