Having recently gone through the template for this, I can say the template does support what you are wanting. However, there are a couple catches. The first and most prevalent is that the GTS validator will not validate the implementation unless the code is directly on the page, not through a TMS. This includes Google Tag Manager, which doesn't even fully support this.
I believe customers have gotten around this by hardcoding the sample code on test pages so that the validator will recognize the code. Then they are able to control it via Tealium.
I would recommend reaching out to your Account Manager to loop in one of our Solutions Engineers to help with the set up. There are a couple mappings that need to be manually set up, which aren't available via the E-commerce Extension.
I have not heard of any changes with Google. I was on and off with this project because we had a Solutions Engineer do the implementation. We did add the sample code to our site because we can remove it with a simple database change. But I believe this can be done to a single test page and have Google validate the test page as stated by Jared. With Google validating against the test page the rest of the site can be implemented via Tealium.
Ah, I see. Thanks for that insight Eric. Google actually just notified us that this GTS tag can now be deployed by a TMS. We'll see about that. I'm working on testing with the Google Validation tool. Thanks!