We strive to avoid GC like the plague in the stdlib, and the language itself encourages users to do the same. I wouldn't go so far as to say that we try to make it hard to use GC in Rust, but we definitely believe that it's currently too easy to resort to it over better alternatives. This is why we're moving it into a library.
No thought experiment necessary, you can do this today in two ways:
1) We have an attribute that you can stick in a module that will throw an error at compile time if a managed pointer gets used anywhere in that module, including in its dependencies. (Note: this is still experimental, and I'm not sure if it actually works yet.)
2) It's possible to write Rust entirely without a runtime, which means your result binary just plain won't contain any of the machinery for GC, tasks, or TLS (task-local storage).
This second approach does have consequences. Bad: random bits of the standard lib won't be usable, since our preferred means of error handling uses TLS (and some functional/persistent datastructures will use GC to handle cyclical pointers, since that's our only internally acceptable use case for GC). We have plans to look at dividing the stdlib into "usage profiles" to allow users to selectively disable certain runtime features while still remaining aware of exactly which pieces of the stdlib are still usable.
But the good consequences of disabling the runtime are that if your code exposes a C ABI, then you can write a library that can be called from any other language with a C FFI (i.e. basically every language, ever). This is actually one of my favorite things about Rust.