Hello OP, I work at a call center like place. During the interview I was open about being a person who stutters. Then they hired me so I think being open helped a lot. I do not tend to disclose while calling but I got used to calling and being more confident, so I do not tend to be bothered by it. Do not let it take you a different direction. If you are not confident, it will show and can turn people off. Like Hedgehogs said, any hesitation can be a deal breaker