Has that film ever been released with that scene intact?
On home video? No.
- The 1980s/90s VHS releases came from an old 35mm print, missing the "Hitler" scene.
- The 2006 DVD was sourced from a new master print, taken from the only surviving nitrate negative in Warner Bros.' vaults, but it does
not include the puzzle payoff gag. *
Does Ted & Larry's "Hitler" clip still exist?
Yes, but only on old 16mm and 35mm prints from no later that the early 1970s, from a source print/negative that no longer exists.
Unfortunately, when Warner Home Video released the restored nitrate-sourced version of DANCING LADY in 2006, they made no attempt to re-insert the missing scene using one of those old 16/35 prints.
* Common practice in the early/mid 1930s for the studios to exise topical and political references from copies of their films... to satisfy/pacify isolationist sentiments in certain markets, e.g., middle America. MGM cut the "Hitler" reference from some markets' versions of DANCING LADY. Unfortunately, the edited version is the only nitrate negative that survives in Warner Bros.' vaults today.