for string that are utf-8 (of course)
Yes, of course. There are many things you can do with strings though. UTF-8 is backwards compatible with ASCII. If you only want to operate on the ASCII characters of a string, it may or may not make a difference. It depends on what you need to do with your strings.
If you want a direct answer: No, you should not refactor every function to an mb_
function, because it's likely overkill. Should you check your use cases whether a multi-byte UTF-8 string may impact results and refactor accordingly? Yes.