It's like a mini carburetor piggybacked to the main one. That's why it's strictly called an enrichener circuit rather than choke.
It pulls fuel up from the float bowl through that brass tube in the corner. If the bowl gasket is compromised, an air leak will result along with loss of suction.
When the butterfly is closed, there's no venturi effect to draw fuel through the main carb jets, so there's a bypass circuit through the enrichener. That's the large opening in the carb throat entrance, and you can see it's pointed right at the enrichener. From there it exits on the engine side of the butterfly.
And yes, it will flow more fuel as the lever is gradually opened and none when closed (blocking off all air flow through that system).
Wanted: Dead, smashed, crashed or trashed gauges
BMW GAUGE REPAIRS - TACH*SPEEDO*CLOCK*VOLT METER *PODs & LIGHT BOARD*