Imo, anxiety and stuttering are not interconnected like that. If that was that case then the cure for stuttering would be anxiety medication and people who have anxiety would also stutter. It can help. I've stuttered in situations where I was not anxious. It's not that simple. If working on anxiety gives you a better quality of life, then go for it, but it won't cure stuttering. Contrary to what the consensus is, I stutter when I'm alone, when I talk to animals, and when I sing/rap at times.