When people claim "Rust is secure", then what they mean is that Rust makes it very difficult for developers to create bugs which could result in security vulnerabilities like buffer overflows or use-after-free.
But those aren't the vulnerabilities cheater use.
Cheaters use techniques like:
- Patching the game executable
- Injecting code into the game executable by replacing DLL files
- Replacing assets
- Reading and changing process memory
- Simulating inputs
Rust does nothing which makes any of that any easier or harder to do.
One argument you could make is that Rust is relatively new, so the tools to reverse-engineer applications written in Rust are less mature than for languages like, say, C++ or C#. But that's a security-by-obscurity argument which can easily change when people start building those tools.
So tl;dr: No, using Rust does not prevent any cheating.