Why, yes! FullStory can capture both Web Components and, by extension, Shadow DOM.
This means if you're using custom components or a framework that relies on Shadow DOM, you will be able to see those elements clearly in FullStory—both in session replay and as elements available for OmniSearch and segment criteria.
For a more complete list of all of the frameworks and other browser quirks that FullStory supports, please see this article.