..at what point of copying the files onto your machine could you say "I have installed OS 3.9 on this machine...."?
You can say you've got 3.9 when you can use programs and prefs using Reaction GUI (damn thing won't work with 3.1), when you can see Colouricons (without converting) and when you see Amiga International in the Workbench>About instead of Commodore-Amiga.
Without this, you're still running 3.1 (...and you're probably better off anyway).