You are correct, current clamps can't read accurately in this situation. All you'll get is any disparity between the phases, which, will be small.
That said, it's probably worth a try, because it's likely that internally the drier's control circuits are only tapping one leg, and you might be able to read that, and it might change reliably enough to trigger an alert.
Usually, you'd use a vibration sensor for this job however. You can also use a thermal sensor on the exhaust air, combined with a time delay (because they run cooldown/dewrinkle cycles), and you're good to go.
That said, it's probably worth a try, because it's likely that internally the drier's control circuits are only tapping one leg, and you might be able to read that, and it might change reliably enough to trigger an alert.
Usually, you'd use a vibration sensor for this job however. You can also use a thermal sensor on the exhaust air, combined with a time delay (because they run cooldown/dewrinkle cycles), and you're good to go.