You would need to consult the agreement. You are signing a contract that contains the terms that your are agreeing to within it.
You may still receive unemployment if you are not let go or fired for cause.
The terms of your agreement should be reviewed carefully by you and i urge you to seek out an attorney to get a second opinion.
A severance package normally will not prevent you from qualifying for unemployment if you are otherwise eligible. A non-compete cannot be overbroad in area or time, however if you are in the same close geographic area it is probably valid for a period of time. Keep in mind client lists are tradesecrets and use of them may open you up to litigation. You really should consult an attorney on these matters especially if you are planning on opening your own business. An attorney can assist you in building the right foundation for your business and protecting your future interests.
This response is informational only and not legal advice. Further, this response does not establish an attorney client relationship.