I've done this! Given the right interface I was surprised at how well it did. Prompted it "You're controlling a character in Old School RuneScape, come up with a goal for yourself, and don't stop working on it until you've achieved it". It decided to fish for and cook 100 lobsters, and it did it pretty much flawlessly!

Biggest downside was it's inability to see (literally), getting lists of interact-able game objects, NPCs, etc was fine when it decided to do something that didn't require any real-time input. Sailing, or anything that required it to react to what's on screen was pretty much impossible without more tooling to manage the reacting part for it (e.g. tool to navigate automatically to some location).