Dynamic adds saturation to whatever is on the screen. Movie and Professional lower the saturation settings as well as add somewhat of a brownish greenish tinge to the display to mute colors further. The AMOLED screen technology that is utilized in the Note 3 uses power for any pixel that isn't completely black. When you pull up a black image on the Note 3, it will look like the display is just off. These screen modes wouldn't affect battery life in any significant way because there are still pixels being lit up as long as you have anything other than black on the screen.
tldr: no