I think it definitely matters and opens up a lot of networking opportunities with faculty, students, and professionals in the community. It shows your investment into the field and you can speak to specific experiences in your letter. Also, I think if you plan to apply to your current school, it'll be one other involvement that will make you stand out from other applicants applying to the program.
I was fortunate enough to serve on my school's NSSLHA board and loved it. If you're doing it for the right reasons, then it will only benefit your app