Is it possible at all for the stuttering to just stop all of a sudden on its own?

Stuttering: There are 2 types of stuttering. First type is when the stutter is only at the beginning of a sentence. The second type is when the stutter is present throughout the sentence. The first type often will go away on its own without therapy. The second type rarely goes away on its own and almost always needs speech therapy. So the answer to your question depends on which type of stutter.