Your severance agreement most probably states that you should see a lawyer before signing. Even if it doesn't, you definitely should. As far as unemployment, it does not matter what the agreement states. Unemployment will make their own determination based on the actual facts and circumstances that caused you to apply. You will be eligible for unemployment if you are being laid off without cause.
Generally speaking, such severance agreements have been held not to be a bar from receiving State unemployment benefits after exhaustion of any payments that can be considered salary payments. My answer, however, is limited to what's stated in your question. An attorney would need to look at the entire agreement in order to give you a more informed opinion.