Seems pretty clear to me from your first sentance: "...has a policy of 'no weapons' of any kind on their property. That include the parking lot and buildings..."
Obviously they have given you notice of their wishes, and of their intention to terminate anyone who violates the company policy. It is their right to dictate their terms, on their property. It is subsequently your right to find another place to work, or submit to their property rights, against your will, because the income is worth the sacrifice.
If you refuse to leave after termination, when discovered with a firearm, that would be paramount to trespassing (an arrestable offence). So, yes, blatant voilation of another's property rights is illegal. However, if you can legally possess a firearm in your locality, there is nothing illegal about having it. The Police DO NOT enforce company policy! They only enforce law, so you are only in jeopardy if you break a law, with your gun, on the company's property.