I don’t think you can change the value the by default to “NO” instead of “Yes”. If you don’t want the task to be published, then just simply save the project to the server without publishing it.
Here at QC, we created a special “Publish Info” view for our PMs which lists all the tasks in a plan with the "Publish" column exposed. Our PMs were trained to select the task(s) which they don’t want to publish to “NO” manually. So far, it works well since they rarely don’t just publish a plan while there are specific tasks which they don’t want to be published.