Yup what you have there is an automatic fuel cutoff or vacuum shutoff. They go by a variety of names.
It's essentially a second fuel valve, that only opens when there's vacuum being drawn at the carbs, i.e. engine running.
Looking at the diagram posted earlier, fuel comes from the fuel tank's petcock via hose #7 to the vacuum shutoff valve, and when the valve is open it can pass through to hose #2 and flow to the carbs.
The diaphragm sits in a little chamber, dividing it in half. The spring pushes against the diaphragm keeping it's pin in the valve body and closing the valve. Vacuum is brought to the valve via the smaller hose #3 and draws against the diaphragm, compressing the spring and opening the valve. Hose #4 is a vent that lets air into the other side of the chamber when the diaphragm moves, otherwise it would vacuum-lock and wouldn't be able to move.
So, you can omit this whole assembly, run hose #7 straight from the manual petcock to the carb's fuel inlet, and then cap off the place where you unplugged hose #3, otherwise you're have a huge vacuum leak there.
Remember to shut off the fuel when you park the bike, if you do this, otherwise if a float valve gets stuck you can drain all of your fuel out onto the ground or into the engine.
If on the other hand you'd like to keep this valve, I'd recommend considering a new diaphragm, yours looks like it has a tear along the edge. Any vacuum leaks or grit inside this thing will cause you headaches later from poor fuel flow.
mystic_1