While generally true this doesn't apply to the upgrade, preferred/ELR seating, and priority boarding benefits. But as a 1K, you will be behind Platinums for upgrade priority on sCO flights (at least until the systems are merged).

I'd recommend matching your 1K status to CO Plat at united.com/linkmyaccounts and use your new CO Plat # when flying on sCO metal.

Also you only show up on the Upgrade Standby List once you have checked in for your flight. Moreover, note that this list isn't used until checkin closes. The GA will then process remaining upgrades according to the Upgrade Standby List. (Prior to that EUA handles all upgrades, which prioritizes by a slightly different method—the final tie breaker is time of checkin rather than time of purchase.)