Google document's picker doesn't allow the user to search for documents.

The google document picker doesn't allow you to place your cursor in the title contains search box in either Confluence or JIRA.

To reach the document picker from JIRA you need to click 'Attach Google Docs' in any JIRA issue on an OnDemand instance with Google Apps integration.

To reach the document picker from Confluence you need to edit a page and then insert the macro 'Google Document' and then click 'select document'.