No, old electrical appliances like fans are not harmful to use if they are not connected to a source of current (electricity). When an electrical appliance is not connected to a power source, it is effectively disconnected from the electrical circuit, and there is no flow of electricity through it.
As long as the fan is not damaged or compromised in any way, it should be safe to use as a simple manual fan (by physically moving the blades). However, keep in mind that some older fans might have sharp edges or moving parts that could pose a physical hazard if mishandled or used improperly. So, while they are not harmful from an electrical perspective, it's essential to handle any old appliance with care and follow the manufacturer's instructions and safety guidelines.
If an old electrical appliance is damaged or appears to be malfunctioning, it's best not to use it until it has been properly inspected, repaired, or replaced by a qualified professional. Electrical appliances can pose safety risks when connected to a power source if they are faulty or damaged.