Joining a bunch of clubs that don't mean much to you on top of your main extracurricular activities will not help your college applications. If anything, it could actually hurt you in the application process. Top colleges are looking for students who are passionate about the activities they pursue in high school. If they see that you're a member of six different clubs that each meet once a week, it will be pretty obvious to them that you're just trying to pad your resume. I'd actually argue that Student 1 in your example would look better to colleges because he didn't waste his time trying to game the system with added extracurricular fluff.
Instead of joining clubs that have no substantial value to you, I'd recommend taking some time to think about which extracurricular pursuits really interest you. If you're looking to attend a very selective college, you should try to accomplish something substantial in one or two main areas rather than spreading yourself thin. Read this article for more advice on how to set meaningful extracurricular goals and give yourself the best chances of acceptance at the most intense schools.