What I told you will work fine - IF - you have the 3.1 ROM installed. None of that will mess up you setup however. Good luck
Go ahead and upgrade! 3.1 will make it much more user friendly setup, and it will still play games, and serious applications. Any old games that don't want to run on 3.1, just run Degrader and they will work.
Still easier and quicker to just get an A1200 to do that. Harder to get an Amiga 2000 with a classic set-up. Not exactly the original but certainly closer to the purity of the 2000 era than the 3.1. I wouldn't swap out a 2000 for an OS that meant I had to ever degrade it, whether hardware or software. Leave it commando and save the classic computer for a future generation so they can enjoy what it was to use an A2000 with the OS as is. There really are way more convenient Amigas that can run 3.1.
I guess I am just sensitive to any prospect of breaking these beloved machines given that I have recovered way too many in my time from folk that had great ambition but gave up and detroyed the computer as a consequence. I am not suggesting any failure by the current owner I am just encouraging the guy with the classic car not rip out dashboard cus a more modern one looks better. It really is very hard to gets things back the way they were.
Everyone to their own I guess.