Yeah absolutely. Most undergrad work is free. Specialty work may cost you something, but it's a case-by-case basis. I've had classmates have their 3rd extracted for free, invisalign for free, but you may be charged for comprehensive ortho work (if you're case isn't good for invisalign).
I got my wisdom teeth out by the oral surgeon at my school for free. A few of my classmates got braces for free. It's definitely possible, but I'm not sure if it varies from school to school. Check with a dental student at the school you're interested in and ask.