Based on what I've read, it's entirely possible. If my Rust knowledge is correct, there are 2 things that have to be proven - the object's lifetime and the borrow rules.
Proving the lifetime can be done at compile-time based on what was discussed in these articles https://without.boats/tags/shifgrethor/. But that still leaves us with proving that we don't violate the borrow rules. AFAIK, the only way to do it in my implementation is with Cell and RefCell enforcing the borrow rules at runtime.
Before removing all the safety checks, I actually used Gc<RefCell<T>> for mutable objects, so the borrow rules were enforced but not the lifetime. However, I decided to remove RefCell<T> to have some fun and see how I could shoot myself in the foot.