The site  variation feature is used to publish content from a source variation to target variations. The target variations  don't have to be styled like the source variation, but the content types need to be the same, and they all need to be publishing sites. Variations are a publishing site capability.

If I understand your question correctly I'd answer it like this;

You definitely can't just create a top level publishing site with a series of non-publishing subsites and expect Site Variations to push content down to them.

You can create a publishing site and define variation labels, and the variation hierarchy. The publishing subsites that will be created for you will be able to have content published to them from your source variation. You'll also be free to create Team Template subsites etc within that hierarchy, BUT you won't be able to use Variations to publish content to those non-publishing subsites. There's no way around that.
You might be able to implement some custom development to grab content from your Target Variation and put it into your Team sites  etc. It would be tricky though, and I don't see how you could easily maintain any mapping between the Target Variation content, and where exactly it should go in your Team Sites.