I do not believe so as the port which is exposed by the container is HTTP (80). From the perspective of the container, the traffic it handles is HTTP.
I have the same setup as yours, with the difference that the container is not available to the LAN at all and all traffic must go though the reverse proxy, which in turn only exposes HTTPS (and of course terminates it).
So at least the web interface should be able to handle HTTP.
EDIT: also please see Ver 1.15 requires ssl for web vault