I looked up the policies regarding leaving the company, and as someone mentioned above, it was all very confusing.
So I called the hotline, got transferred to our benefits center, where I got told that I need to ask my manager about what happens to the vacation days I've bought.
At this point, I'm assuming that if I don't use those vacation days, I'm going to lose the money, so I plan to hand in my letter stating what my last official day will be, but my last day in the office will be a few days before that. If for some reason they have a problem with that, I'll adjust accordingly.
A few people I know in real life, who don't work here, have brought up that sometimes when people hand in a resignation letter, they are escorted out that same day. There's no history of that happening here, as far as I know, but now I'm all paranoid. But I feel I do have to give the 2 weeks notice.