Not necessarily but for me when I copped a fight stick not only did I get better at fighting games but I enjoyed them a lot more. I have the same stick you listed above and it's honestly one of the best gaming purchases I made this generation. You're not gonna become a top tier player overnight but I guarantee if you put in the work you're not gonna wanna go back to playing on standard controllers.
With that said I don't enjoy playing all fighting games on stick specifically the
Dead or Alive and Mortal Kombat games. Some games just feel better on pad for me at least. Tekken 7, Killer Instinct, and Virtua Fighter 5 Final Showdown on the other hand feel just right on stick.
One last thing , fight sticks can also be used to play shoot em' ups, most retro games , and a few platformers so that's another benefit. If you're still skeptical and don't wanna pull the trigger on a stick look into fight pads. I hear the
fighting commander is a solid option.