Unless you are going to review the whole code, written from scratch, there is no way to actually be aware of all allocations in Rust without help from a memory profiler.
For example:
T t;
a = b;
T t2 = t;
let t: T; // won't allocate
let t = T::new(); // might allocate
a = b; // won't allocate
let t2 = t; // won't allocate
let t2 = t.clone(); // might allocate
There are a few places in C++ where allocation can happen pretty much invisibly. A copy constructor is an example of that. You might see a new allocation simply by calling a method.
With rust, you usually won't see an allocation unless it is explicitly called for. You can follow the call tree and very easily pick out when those allocations are happening.
The C++ copy constructor comes up fairly frequently.
You would need to ignore the documentation and bend over backwards to use it for an actual type conversion, because you can only return references.