Well...
NO it does not work... but there is at least the "option" to select such behavior... 😉
I personally used TB (I'm working primary on a Linux desktop) before (on the old server) and switched to Grommunio web to have all features available (contacts, calendars...) and noticed this "inability" to store replies in the same folder.
None of the other test users (mainly Outlook) did not complain (jet)... but they will for sure...
Similar topic - read confirmations? Is that working for you?