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.
Please note however, CSS selectors within the Shadow DOM are invisible to the primary DOM itself, which unfortunately means that some Page Insights tools such as Inspect Mode and Click/Scroll Maps specifically, are unsupported in FullStory if your site is utilizing Shadow DOM.
For a more complete list of all of the frameworks and other browser quirks that FullStory supports, please see this article.