Hey Ian -
Sounds like your users are Excel-addicted?
This is a pretty common request from people who haven't made the mental shift away from "drop everything in Excel". However, Tableau isn't really built to be a "poor man's ETL tool", ...so data dumping doesn't get tons of love.
Anyway, short answer is "No". The user would need to "View Data" and then choose to save as CSV.
Essentially, your users are going to be fighting the intended behavior of Tableau - to do analysis inside Tableau itself rather than use it as a tool to choose & dump data fields from.
Sorry and hope that helps a wee bit?
Thank you for the quick reply. I figured this was the answer and the users will just have to live with it. Thank you for the information/confirmation/proof.