Would making short films help boost a career in film making?

Taking the initiative to do things on your own always looks great on college applications. If you can do the work, why not? You can only learn from experience. Even failure has something to teach you...if nothing else, what not to do.
If you do decide to make these projects, I'd recomend going all out and doing your best. You can even make these projects union under the new media contracts provided for web productions. Go to the SAG-AFTRA website: https://osa.sagaftra.org/ and fill out all the paperwork. It may even help to make your project better to have all these steps complete before you begin.

A lot of film making is simply due diligence. If you start something, finish it. Break a leg!

Absolutely! In fact, making films is really all the education that you truly need to get into film-making. That's not to say that there isn't validity to getting an education in film-making, but I've never (in 15 years) heard anyone say, "hey we should hire this person because he/she has a degree from blank college." All anyone cares about in film is what your portfolio/reel looks like. If it's amazing and you did it by yourself in your basement, then it's all that more impressive than doing a small subset with a group of 10 other students in college. However, the work that most people can do on their own is generally worse than that which someone can do in a group with like-minded students at a quality university with resources and support available to them. At the very least, making your own films would better inform you if it's something that you truly want to do with your career as well as help you decide which aspects are most interesting to you. For instance, Directing, Writing, Acting, VFX, Editing, Producing, etc... There are many facets to film-making and certainly no-one is truly exceptional at them all.