True.Unless the watch is connected (paired) to the phone. In that case, the alert will come through the phone to the watch and avoid any potential use of the watch's cellular capability.
Interesting. Maybe consider turning of wifi on the watch to see if it's actually using cellular rather than wifi.I just found this: https://groups.google.com/forum/#!topic/misc.phone.mobile.iphone/vfQTa6Hdv40
It appears that a cell phone without a SIM card can still receive Amber Alerts. As a test, I'm going to leave my phone in Airplane mode this afternoon, and see if the alert comes through to my watch. The test is scheduled for 2:18pm EST, Oct 3, 2018.