Well I still stutter when reading alone. Not stuttering when alone or when speaking to pets is not the case for every stutterer. And yes, I do believe it's possible. If you keep practing saying your problem sounds in a deliberate manner, focusing on improving awareness of speech articulators, your brain will adapt, and you'll have more coordination when making speech sounds. This is known as speech sound stimulability and it has some amount of scientific research backing it. Hollins Stuttering Institute uses it, and some speech therapy programs use it.