Well, you will basically get a higher data rate, which could be quite useful for underwater video (there´s quite a bit of camera movement). Now, you will NEED to apply a color correction filter in Premiere. I am not familiar with Premiere Elements (or Premiere even), you should definitively check before heading off to Roatan how the whole workflow works for you. Even if not underwater, shooting stuff around both interior and exterior shots will give you a good idea of what CineStyle (the ProTune is basically CineStyle color setting for the GoPro) can do for you and what kind of post-production advantages it will give you.
Im not going to get very technical because I would have to double check some of my facts, but I can give you sort of an explanation "for mortals" about the type of encoding a setting like ProTune provides. When you are working with professional grade digital cameras (an Arri Alexa for example), you want to have as much information as possible available. This is NOT automatically going to produce a better quality image on itself, but it will give you post-production "freedom" to tailor it to whatever your heart desires.
Before ProTune (or with Protune turned off) you would get a predefined color/sharpness/contrast encoding that would be the "accepted general standard" of what people usually consider "good looking image". Now, this MIGHT NOT BE the look you are aiming for (let´s call it high contrast, good amount of chroma and quite a bit of sharpness). Then you would have to work with an already "processed" image to be able to achieve the look you are striving for. This "look achievement" thing is usually called COLOR GRADING. It will balance out the different settings (chroma, color, luminance, sharpness, contrast, etc) and achieve a certain look. Without ProTune, you need to work AGAINST the default setting and you loose some quality and the maximum limits where you can work get reduced.
With ProTune you get a FLAT IMAGE. It has settings for contrast, chroma, luminance, color, etc that are very NEUTRAL. They are optimized to be able to achieve the best balance for working the COLOR GRADING the way you want. The objective is to keep all values in a point where you have the most control in post-production to have as much information available so you can "move around the look of things". This is very good if you know what you are doing. And your software has the ability to work this values, and you can efficiently copy, paste and retouch the setting amongst different clips and cuts. Not a lot of video editing software has this capabilities, or has them available in an "efficient and usable package".
ProTune is a great addition to the GoPro, but I would´t recommend it to a vacationer just wanting to get underwater shots. It will certainly double and probably quadruple the amount of post work you have to do on whatever you do. And you NEED to be confident about your abilities in managing color grading. Of course anyone can learn anything. But if you have never fooled with color grading, it´s going to be frustrating. So baby steps, take on maybe only one day of ProTune and then work with that to learn how to do color grading (if your software even supports it).
Also with ProTune you get a higher bitrate (more information is actually recorded in terms of compression, this is good of course, but will also eat up your cards and make the whole video bigger).
It´s hard to explain the use of something like Pro Tune when you don´t understand the whole digital cinema acquisition workflow. But this is the best I could do to explain it in a nutshell for a diving forum. If you have questions on these things, feel free to shoot them and I will try to rephrase to answer them or answer new questions.