I wouldn't delete anything until you get the new add-on published, or at least make a copy of the Apps Script file. You can certainly publish a new add-on, and publish it as being public. You can publish multiple add-ons. It doesn't matter if they are identical or almost identical. You can publish an add-on as public but unlisted, so in the future, you could publish it as public but unlisted. And you can uncheck the box to "Unlist Application" and then update the change. So if you could first published it as unlisted, and then when you wanted it to be public, then you could uncheck the box so that you wouldn't need to delete it, or publish a different add-on.