The jurisdiction of these courts varies from one state to another and the answer depends on a number of factors. If the company does business in the jurisdiction of the small claims court it should be possible, but there are several other details that influence the final answer , such as the nature of the suit and the amount of damages you are claiming. I would ask a lawyer about this, it might cost a couple of hundred $$ to find out, but trying to sue someone without understanding the basics is a real waste of time and money.
You cannot sue a company in a Small Claims Court. This is because this court specializes in petty cases that do not exceed $10,000. This means the case can be quickly solved. Get the list of the cases that can be solved by this court on http://www.lasuperiorcourt.org/smallclaims/ui/.