So putting effort into the application now can mean more time to focus on the product later if I'm accepted.True, but remember you're riding on the "if I'm accepted" part. It's highly unlikely that you will be, especially if your application lacks the knowledge you're likely to gain during the process of developing your product. I'm not saying that it doesn't make sense for you to apply. Just keep in mind that every second you spend doing A is time that you could have spent doing B.
While I won't say I hated college, I was eager to get out and start my own company from day one. I seriously considered it a few times, but I'm glad I didn't go through with it. College has a lot of resources that are harder to come by on the outside. (I just graduated a few months ago, so it could be that I'm wrong and the resources are just as easy to tap into, but I haven't figured it out yet.)
Take advantage of the fact that other people are taking care of your finances, and spend your time improving yourself. Take advantage of the fact that you're surrounded by students who are quite possibly as ambitious as you, and make some connections with promising people. It could pay off in the future. I really recommend working on small projects during college, instead of trying to create an actual startup.
Sure you probably won't make money from doing this, but there are other benefits. Small projects don't have to be time-intensive, so you can still pass your classes and enjoy college life. They also provide a really good excuse for you to sit down and work alongside one of those promising classmates I mentioned earlier. Plus, taking a project from the initial phases through completion is bound to be a great learning experience. The phrase "learning experience" is a bit cliche and overused, but trust me, this is truly a field where learning pays off.
Also, consider the fact that all these talented people starting companies are really just out to make money. This limits their choices, consequently creating a large space out there for apps that aren't designed to make money. If you do a good enough job on the right project, you stand to gain a lot of attention, respect, experience, and opportunities.