Not really, at a certain amount of current (how much exactly depends of the shape and material of the superconductor in question) it "quenches", where it abrupt

Not really, at a certain amount of current (how much exactly depends of the shape and material of the superconductor in question) it "quenches", where it abruptly goes back to being a material with non-zero resistance. Since there is usually a ton of current already flowing through the material, this usually leads to damage as the former superconductor heats up rapidly. See also https://en.wikipedia.org/wiki/Superconducting_magnet#Magnet_quench https://en.wikipedia.org/wiki/Superconducting_magnet#Magnet_...