I don't think this is correct. The shot-to-shot time when using a flash *might* be longer when using alkaline AAs, but so long as the camera has enough power to operate, shutter speed and shutter lag shouldn't be affected.
If this were the case, you'd also see increases in shutter lag as your rechargables wore down, and I've never noticed that. IME, the camera continues to perform "as normal" right up until you get the "Battery Low" message and then it turns off....