There is zero guarantee about that. The result could have fewer vulnerabilities, but it's not an easy thing to do. I'd say there definitely are some vulnerabilities left in sudo code, but over the years all the obvious bugs have already been eliminated and rewriting it in a new language can reintroduce a lot of those. Now, if the people doing this are competent and have time and money in their hands, rust enables doing some things better and basically lets you forget about basic and advanced memory bugs, so the final product may well be a good (better) one.

But just using another language to reimplement something in order to make it "safer" in some abstract manner does not guarantee anything. Good coding practices combined with "elementary" and highly-portable language like C can also result in victory that can't really be challenged. We'll see.