If the safer type system gives the devs an unwarranted sense of security, they might write less tests, be less careful in their design, or wait longer between audits and other sanity checks.
If on the other hand the devs understand which classes of bugs aren't ruled out in Rust, then sure, you will end up with fewer bugs.
Rust's type system eliminates the need to test for whole classes of bugs, because they are statically checked for at compile time. This means that tests can be more focused on logic errors rather than standard book keeping. If you look at the example set by the rust repository itself (https://github.com/mozilla/rust/), it is heavily tested and every single PR (https://github.com/mozilla/rust/pulls) is reviewed before merging. This discipline definitely filters down into third party libraries.
If on the other hand the devs understand which classes of bugs aren't ruled out in Rust, then sure, you will end up with fewer bugs.