If I refuse to sign a non-compete contract and get fired can I still collect unemployment benefits?

I have been employed at my current company for over a year. I work in fine jewelry sales as a sales associate in a privately owned jewelry store. My company recently decided to draft and force us to sign a non-compete agreement. While I agree with about 95% of the contract there is a portion that says I wont be able to work for a period of a year in the capital district for any business that the company deems as competition. I have expressed my discomfort at signing this as I have been working in jewelry sales for 7 years. My boss refuses to strike that part from the contract but has offered to lower it to six months, which to me is still unacceptable. They told me that if I do not sign this that I will be fired. I do not plan on signing it and I want to know if this means I wont be able to collect unemployment insurance. Thanks for your consideration.