No as far as I can tell this is not possible - because web components with shadow dom do not leak implementation details.
For example you have <video> tag - it has its own internal controls that are not part of the markup - same with web components - <my-custom-elem> is what the browser sees - not what is inside - for it it is just a DOM element.
Then again I haven't explored the subject too deeply since I do Python server side so js rendering is not an option here.
I suppose it would be possible if you would drop the shadow dom from your elements.
For example you have <video> tag - it has its own internal controls that are not part of the markup - same with web components - <my-custom-elem> is what the browser sees - not what is inside - for it it is just a DOM element.
Then again I haven't explored the subject too deeply since I do Python server side so js rendering is not an option here. I suppose it would be possible if you would drop the shadow dom from your elements.