One of the main upsides to being out of school and working full-time is that I rarely, if ever, have homework, and my evenings and weekends belong to me. Time management is an important skill - think of your time like money, or any other resource you have. You get to choose how to spend it by weighing what's important in your life and how much time you want to dedicate to it. Being in this unit is not at all like a second job (can confirm, have worked two jobs, and have also played EVE Online) - your time commitment to the unit tends to only be about 6-8 hours a week, provided you're not in a leadership position or have additional responsibilities.
That said, as fun and rewarding as being in this unit is, I wouldn't rank it above school or work, which were your two main concerns. Never let gaming get in the way of making responsible life choices. If you want to and are able to carve out that much time, then feel free to apply and join, but please don't let the 506th come between you and your hopes and dreams.