Yes.
not quite.
A Bain -Marie is indeed a waterbath mainly used as a temperature buffer between a hot oven and the thing being cooked, or as a means to hold food at a hot temperature without getting it hot enough to burn.
Water boils at 100C so if you put a creme brulee for example, in a bain marie
inside an oven it takes a lot longer for the temperature of the brulee to get over 100 degrees. (egg starts to denature and coagulate at around 70C so without a water bath, if the oven is too hot it's next to impossible to cook a creme brulee in a "normal" oven.*)
A souffle mixture is basically "eggy foam" and when cooking souffles in a bain-marie the water does 2 things. first it prevents the souffle mix from getting too hot too fast and secondly the steam generated increases the temperature of the oven and the ovens ability to transfer heat. This hotter temperature helps the souffle to rise faster, as well as setting the outside of the mix crispier to hold it's shape.
Things rise when the tiny air bubbles contained within the mixture increase in size. The hotter the air temperature of the oven the more the bubbles can expand before the protein chains in the mixture solidify and lock those bubbles into place.
(you introduce steam into an oven when baking bread for the same reason, to increase the air temperature and 'carrying capacity' of the air to make the bread lighter and it's crust cripsier.)
* In more recent times commercial kitchen equipment has a lot greater degree of control over temperature. You can now set an oven easily to cook something at less than 100C, as well as inject steam on demand, so nowadays bain maries aren't used that often.
