Interesting concept. Tableau creates vizzes on a static set of data. Whenever you change a filter or interact with a view, I don't believe you force a refresh on the underlying data. Unfortunately, I'm not aware of any way to force refreshes on the data itself, which would update your NOW() function result.
If you are using Tableau server, you might be able to use some sort of url parameter. List of Embed Parameters
(http://server.domain.com/views/Workbook/View?:refresh) or change a setting in the server configuration, but nothing is really coming to mind.
I wondered if a rawsql_datetime("now()") would work. No. It refreshes in the same way without an extract. With an extract, it becomes materialized and will not update without an extract refresh.