They have the ability, but it doesn't mean that they have a restiction. You would have to verify through your company. From my interpretation they have the ability to impose a ban.
That's what I gather from it all. Really would need some clarification on the matter I am not certain that they can't impose criminal charges. Kirk Freeman is very legal savvy he could possibly shed some light on the subject.
"They"? You mean the company? The company cannot prosecute you for anything criminally.
However, the Prosecuting Attorney could file Criminal Trespass. I've never seen it in 16 years but if we are just free associating then potentially Criminal Trespass.
If your employer is the federal government then you face the entire panoply of the United States Code or the UCMJ depending on: where you are or which agency you are with.