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I'm going to respectfully disagree with Dan. Whereas, I do not have a true stock engine, I do have a VMAX ported/polished TB and a CorvetteMod CAI shroud. I purchased a Diablosport inTune and custom tune from Lew. The car drives night and day from its stock tune. From what I understand, it probably gained 10-20 HP, but the throttle response and tranny performance (shifting firmness and speed) is very noticeable. It drives like a different car, basically like a Corvette should drive like.
I purchased and installed a throttle controller. This controller really changed how the car reacts to the accelerator. You can dial in the feel that you desire for throttle response. A great addition to Lew's tune.
On an all-stock car? No; at least that's what I was told by a tuner in your state for my car. And you do realize, potentially, you impact your powertrain warranty with a tune, right? If that's ok with you, and you can pass emissions/inspections, I'd go with headers and a tune, not just a tune.
For your own information, ask the question of forum vendor and tuner in Cream Ridge, ECS (East Coast Supercharging)---how many rear wheel horsepower will I gain with a tune on my stock LS3?