I didn't use a laptop for a year because my laptop was a wreck, and I am in senior year at high school. I have an iPad, so I had to do everything on my iPad. I managed to watch movies and TV on it thanks to netflix, I read books and PDFs on it, but when it comes to assignments and projects, I had to use my laptop - it has a keyboard, printing documents is easier, the screen is much bigger and has much more features on MS office.
I just bought a new laptop that I'm taking with me to uni.
I don't think that you'll manage to go through uni without a laptop, but that's just my opinion.