Yes, but at this point the critical piece that made no-GC memory safety possible - linear types - had already been researched and known in the FP community. Rust's critical invention was "what if we modeled heap ownership and borrowing with linear types".

Okay, strictly speaking, Rust types are affine, not linear. Leaking Rust values is a safe operation. In a linear Rust the compiler would have to prove all values do not leak, but this would be incredibly difficult and probably make reference counting illegal.