Builder Theme Studio works with your theme
Yes, Builder Theme Studio works with any / all Shopify themes. Any themes you've added to your Theme Library in Shopify are accessible in Builder Theme Studio, and you can edit them to your liking.
If you have multiple themes in your Shopify account, you can access and switch between them in Builder Theme Studio.
In the Studio tab, all of your themes are available under "Editing Theme". You'll see a dropdown menu showing which theme you are currently on and your other available themes. Here you can switch between your themes and customize your theme pages and elements.
Note: publishing, duplicating and downloading a theme should be done in your Shopify account.