I think that I could probably survive, battery life aside, but I probably wouldn't choose to leave my phone at home.
Directions, payments, communications, calendars, and notes are the essential things, and especially with Keep single note tiles watches do most everything pretty well.
If I had a cell enabled watch I might consider trying, but I don't want to pay for the extra line, I just wanted to be able to put my phone in a backpack most of the time.
Using them takes active effort though, it's not like you automatically look at your watch for the time or to check a notification, "Check phone" is probably stronger than any other reflex.
Everything else requires at least a tiny bit of thought but "I heard a noise gotta check it" is effortless and you have to actively learn to not look at it all the time or physically leave the phone far away if that's your goal.