If you signed an agreement that stated a clear start and end date and defined your role as an "Intern," you do not qualify for unemployment. If you file for unemployment, the company has the right to dispute your claim and will win because you were hired for a specific time period and not as an "at-will employee."
I hope so. My internship ends in 2 weeks. I have a friend that just got it. So I think the answer is yes.