Yes, they can tell if you opened it. Sometimes the screws are sealed, sometimes they put a small piece of tape, but most companies DO have a security measure and can tell if you opened the case. Call the people first, and if they say to open it for trouble shooting, then you are okay.
Before calling I'd try sending an E Mail so you have something in writing. Given the general level (low) of tech support and customer service, I don't think trust is a good idea.