Yes. Fullstory can capture both Web Components and, by extension, Shadow DOM. However, there are some caveats.
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. However, some Page Insights tools such as Inspect Mode and Click/Scroll Maps specifically, are unsupported in Fullstory if your site is utilizing Shadow DOM.
Note that the first and last portion of the selector (delimited by spaces) must belong in the same document or fragment.
For a more complete list of all of the frameworks and other browser quirks that Fullstory supports, please see this article.
Can Shadow DOM still be captured when ShadowRoot.mode is set to closed?
Unfortunately, if the shadow root is set to ‘closed’, Fullstory cannot capture shadow DOM subtrees because they would be inaccessible to JavaScript (and therefore inaccessible to tools like Fullstory).