I’m renting an older house that has wiring with no ground. I have a paper shredder and a fan plugged into the same receptacle and when the shredder is running the fan runs. The fan is not turned on.
You could always replace the receptacle and, in the process, confirm that the wiring is correct, in good shape, and not worn though and in contact with the box. Also, make sure that the old wiring jacket is in good shape. I've lived in 1910 houses for decades. People do all kinds of crazy things with these receptacles and their boxes, if it even has one. Old knob and tube often just ran directly from the wall, through a small board or similar, and into the lights. This receptacle might not be safe.