normalizing is just an automatic volume knob. All it does is raise the audio in relation to the highest peak. You'd get the same thing if you just pushed up the fader. However, this isn't always a good thing. If you even have one transient that is at -.1dBFS and the rest of the audio is around -18dBFS, and you want to normalize it to -.01dBFS....your audio is just going to increase by .09dBFS. In other words, you won't notice any difference.
Your best bet is to compress/limit the peaks and turn up the volume afterwards.