To be even more certain, just call UAL before you book and ask about NC availability on the flights you are interested in booking. There have been a few cases where phantom upgrade space showed up on the website while UAL reps couldn't actually see (or honor) the apparent availability. If you're thinking that hard about buying a Y fare, best to make sure before you purchase (or at least make sure within 24 hours after booking, and if upgrade space isn't available, cancel your ticket).

Have you looked into the availability of Z fares on the route? Might not be that much more expensive than full Y and you wouldn't need to use any miles.