I imagine you're right, that the Amish aren't particularly interested in online music services, but I remember reading an article that pointed out that the Amish aren't really anti-technology per se, they're anti-labour-saving devices.

The ethos is apparently to work hard and with your hands, and they have no qualms in letting people with physical issues use tech; the example given in the article was a farmer who had arthritis and whose sons had moved out, who was permitted to use a tractor in order to keep his farm going.