Will my insurance go up if i have geico and first speeding ticket?

I'm 20 and I got a speeding ticket for going 13 over the limit, I had seatbelt on and this is my first speeding ticket. I have GEICO, will GEICO find out about my ticket? And if they do, will my insurance go up? I'm also doing defensive driving, if I complete the course will the insurance company still find out?