I don't think it'll get you any points when they're reviewing your app but it'll give you something to talk about in an interview and will show, perhaps, a deeper than average interest in the dispatch/regulation process. It would be something you did that most other applicants have not. From your background, it might also be a good way to jumpstart your knowledge of the part 121 world after your military career.

Is that worth your time and effort?

If you haven't already, take a look at How To Land A Top Paying Airline Job by Rick Hogan. It's $10 on Kindle. It's pretty good at teaching how to turn your experiences into great answers for the "tell me about a time" interview questions. Reading it sooner, rather than later, will help in making decisions such as this as you'll have a better idea of how it can help you in the hiring process.

For example, "Tell me about one of your weaknesses". You could talk about how you felt that your lack of civilian experience felt like a weakness as compared to other pilots with civilian backgrounds so you sought out ways to learn more about part 121 operations including earning your dispatcher certification and include an example or two of the types of things you learned.