Can a tpl.php file be created that can customize the markup of views that are inserted as a Viewfield?

I'm not sure if this is possible, but say I have a customized version of views-view.tpl.php that uses 2 container divs that are used just for styling purposes (adding borders around the content). Let's also say that I want to overwrite the output of views-view.tpl.php with a file called something like views-viewfield.tpl.php that can be used to format any view that is inserted via the Viewfield module. In my case, I would strip out these 2 container divs on every view that is delivered as a Viewfield, as opposed to a Page or Block display.

This separation would be handy rather than individually customizing each view that I would like to insert into nodes via Viewfield. Can this be done?

Thanks,
Erik