No, by embedding a visualization in any website you are creating a link to the content on the Tableau Server. That is true for Pubic, Online and On Premise. You could take a screenshot of your viz and embed that in SharePoint, but if you want interactivity then it must remain on the server. If you want an image, you would not even need to publish to Public. could take a screenshot of Desktop.
Thanks Robin. Unfortunately, that is not the answer I was hoping to hear, but you have been very helpful.