On picture tube, what do you mean it lights? Does the face light, or just the filament in the neck? If only the later, no, it doesn't mean you have high voltage. Filament of picture tube is connected with filaments of most other tubes. Also, it doesn't guarantee your picture tube is any good.
Now, as for a wire being wrapped around a tube, can you send me a picture of this? If this is a high voltage oscilator vs. a flyback, in some instances, they put a spring around high voltage rectifier with a wire connected to it from the osc. coil. It seemed to be used as some sort of kickback voltage. What size of picture tube is it? You must exercise caution when working on tv's. They utilize very high voltages, and you could do great harm to the set, and conceivably, kill yourself. And, just un-plugging the set does not guarantee you have "lost " the hv. These sets need considerably more caution thatn most radios.
