Like you, I wish to make an open world style game one day and I have decided to use Godot for now as I believe it will let me get there. That being said, I am fairly new to 3D game development so take this advice with a grain of salt.
Godot can handle an open world game as much as any other "AAA" engine. The difference is how much work its going to take on your part to do it. When creating a huge game map like in Fallout 4, there are a couple of things that you will have to handle.
Memory Management
The first thing is memory management. When you load a huge map in a game, no engine can handle all the stuff that something like Fallout 4 has all at once. For instance, if you're in Sanctuary, the game is not loading any objects from downtown Boston into memory. Instead, it's only loading some of the surrounding areas(I believe Bethesda's engine calls them "cells"). When you get close to Boston, it unloads the cells around Sanctuary and starts loading the cells around the part of Boston that you're entering.
When you create an "Open World" style game you will have to do something similar. Other game engines have code and Assets to help quickly handle that. Godot does not(at least, not yet).
Floating Point Precision
Another consideration is what's called the "floating point precision" problem. Without getting into the math of computer graphics, the basic gist is, the further away your objects are from the point of origin, Vector(0.0, 0.0, 0.0), the less precise your object drawing is going to be and your player will start seeing your objects clipping and drawing weirdly.
Again, other "AAA" game engines have a built-in way (or something in their Asset Store) that helps you handle this. Basically, it's a piece of code that resets your origin point after your player moves a certain distance away from it. With Godot, you'll have to write something that does this.
Conclusion
So can Godot do it? Yes. But you'll have to keep those two things(and possibly other challenges that I don't' know about) in mind.
You might ask, "Why, if other engines do it 'automatically', would I go with Godot?". I can't speak for your situation, but I have 2 reasons:
1. The other engines might have an "auto-magical" way of dealing with those two issues, but If those solutions don't work the EXACT way I want them too, I'm stuck writing my own method from scratch anyways.
2. Godot is so fast and easy to use, I'm confident that I'll be able to write the code to handle those cases in just the way I'll want to when I cross that bridge.
