No.
When you create an app you get the theme folder from the template. After that you can modify it and there is no link with the template.
In my company we use our own standard theme app to test our standard-page.html and theme.css.
When we change it we use git to pull, copy the whole theme folder and push as suggested here. We manually repeat this process with all the apps that share our standard theme (until the Anvil guys will give us an official way to include the theme in the dependencies).