Yes - A remap will not significantly alter the operating range of the turbo, this is a hardware limitation afterall, although I think the soft limiter is raised slightly in some remaps allowing you to wring an extra few 100rpm at the top end. What it will do, is improve how effective the turbo is within that operating range i.e. dramatically increased boost pressure, fuelling etc., which results in more power within the afore mentioned operating range.
As jonny points out, to improve the operational range of the turbo, you need a hybrid, or a different one altogether.