Can using a pacifier with braces keep the braces from straightening my teeth?

YES! Any pernicious habit (chewing on pencils, fingernails, your hair, etc) can damage braces and/or interfere with tooth/jaw movement. I don't understand why a 32 year old would evidence the behavior of a toddler. This is distressing. Perhaps you should look into why you are still behaving this way, and get help addressing the problem. Don't ignore this.
YES. I can't imagine a situation where a patient would be wearing braces and still using a pacifier. If this is the case, the pacifier use needs serious attention right away.
Why? If you're wearing braces to straighten your teeth, why would you want to stop the straightening process? Counterproductive, isn't it?