With my understanding of how the LS2 functions, yes!!!!
The car follows two fuel programs, one is low octane which the engine defines based on knock and it comes into play with octane of 90 or less, and high octane which is 91 plus. While it could be possible that your car wouldn't trigger the low octane tables on 89, it more than likely would. On low octane your car retards the timing and richens the fuel mixture. This results in less power and lower fuel economy. The real question is, how much power loss and how much fuel economy loss. Some say you can't feel the difference and others say you can. Some say fuel economy isn't much if any changed and others say it's a large difference. There is also the question of what the richer mixture, needed to compensate for the lower octane, does to things like oil life and catalytic converter life.
What I say is, for $3 per tank of gas I'm not giving away the extra performance or chancing engine damage. Plus if there is fuel economy loss with lower octane your real world savings would be less than $3 per tank.