Class C tow capacities are usually for flat tows, whatever the chassis. Critical factor for trailer towing will be limits on trailer tongue weight, typically in the 350-500 pound range, which means 2500-3500 pound trailers. This is a result of the long rear overhang needed to get that big empty box balanced between front and rear axles.
Some super C designs get past this, and can tow really big trailers, others face similar limitations.
Not so much an issue if your trailer is supported by axles on both ends, rather than riding with significant weight on the tow vehicle.