Well it doesn’t hurt, but it’s certainly more important to do this things that students in NHS do. Colleges are going to see your GPA so you don’t need it to show your academic achievements. Most NHS memberships have a service component which you can demonstrate elsewhere.
The one thing it does do is signal to schools that your teachers view you as someone of high character, and are an overall good student.
I know it seems stupid, but you really don’t have a good reason not to. How hard is it really to go to all your current teachers and have them sign your application form.