Air Cut-Off Valve – What Does it Do?

I’m been working on a 2003 350es for a friend of mine and am now into the carb because of some hard starting issues. It acts like it’s starving for fuel even with the choke on when cranking but then smells like it’s running rich when idling. The carb itself was spotless and everythings in spec. I read in the manual that the fuel cut-off valve should hold vaccuum when it’s applied to the hose but should allow air to pass through the other way. This one holds vaccuum but I don’t seem to be able to blow through it? Correct me if I’m wrong; this valve prevents a leaning in the mixture on decceleration to prevent popping? Could it have anything to do with the primary jet and effect starting? It’s a pricey component and he has limited funds.