They might, I haven't been inside one to look. Asbestos is funny stuff. Some of the old ads listed it as a major selling point. People were around it for many years in far greater quantities than we see today with no ill effects. I wouldn't expect to see asbestos in sewing machine wires. There wouldn't be a need to insulate them from heat.
I agree with Joe. Although some might say I'm too casual about it my thought is as long as you're careful you're not likely to have any ill effects from casual contact. Just wash up afterward.
It's a far different story if you're handling the stuff every day though. Then you need to take all available precautions.
Rodney