You can download the app - it remembers PNR's you access with it even if there is no Skymiles number.
I mainly fly First in the USA, but as a WP, was able to select a E+ seat LAS-LAX with an economy booking 20 hours out. No F&B on such a short flight, but the IFE was complimentary in E+.
Note that often a few E+ seats open up closer to a flight with the Medallions being upgraded.
FWIW, I have an AirNZ booking T-T coming up - earn indicated is 1 APD and 7 SP's. I'll be using Velocity where I get 450+ points and 20 SC's.