It does, but it works best if you compile it yourself, strip the engine down and add your own core game code as c++ classes. Not for everyone, but works good for me as I like c++.

If you wanna go straight to the web, probably start with play canvas or even Defold. Godot works, but if your not a c++ guy or dont want to fork the engine, then your not going to be able to optimize your game as much as I have

Do you know of any examples of doing something more complicated like this with Godot and C++ (past the normal docs)?... I've got some existing C++ game engine stuff I'd like to integrate with Godot for managing rendering side of things.