Not without turning it all into a string (and the mess that can cause). Tableau lacks a FORMAT or TEXT function. You could use a parameter to switch between a date truncated to day and the full time, but I doubt it will display in the way you want.
There's also possibly a way you could do it with rawsql calls.
Interestingly this may be possible in v8 as we can set a parameter in the SQL. That parameter could define the date format retrieved.
Yes! I've been looking for that. Just 'followed' my own post. Thx Alex.