No idea what those strange tower people do...if you're en route you'll be fine though. You'll be a lowly d-side trainee and can take off pretty much anytime you need to...One more person in the break bay that isn't training.
Being that you are a trainee, it is really easy to get spot leave (just going up to your supervisor and asking for the days off). You are not considered "useful" as a d-side trainee and therefore days are usually just granted. As far as annual leave, at ZAU, you bid it off in novemberish for the next year. Trainees have their own bid, so CPC bids wont effect you. You will be competing with other trainees for days off and September usually isn't considered prime time, so you wont have any trouble getting the days off.
There are a lot of responses to this post so far, and I'm not gonna lie, I didn't read them all. I'm just going to jump in because I was in the same exact boat nine years ago, although we didn't have a fancy wedding planned so we weren't under a time crunch to reserve anything. That said, the DAY I got to my facility, I let them know I had just gotten engaged and was trying to plan my wedding. They were super cooperative and basically said, "let us know when it is and we will accommodate it". It's not like you're just trying to ask for random time off.. it's a wedding. Your wedding. They should be understanding. I would, however, get to know your NATCA rep ASAP and ask them how best to approach it. Asking management for a day off the moment you walk in the door may or may not be frowned upon, but your FACREP should be able to smooth things over.