No. Dashboards do not currently support in-table search within the table element itself.
The table widget lets users sort and filter (via selectors and actions), but there’s no built-in text search box like you see in the List widget or in the Map Viewer’s attribute table.
At this time, the only ways people work around it are:
As of now, there’s no native planned update from ESRI that adds a search bar directly to the Dashboard table element, this limitation has been confirmed by users and product feedback channels.
Thanks very much for the information, much appreciated.