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First of all, air flow by mass is maybe 10% of the total capacity of the engine, at 60 MPH, before ERG. then, EGR is turned on. (maybe 10% of inducted air?) engine speed cannot change immediatly, either up or down, but the trottle is where it was before EGR and now it has an additional source of (exhaust) gas, engine is doing the same RPM, so Vacuum drops, less air flows through the air flow meter, so ECU cuts back on Fuel.
But now, less heat is supplied because there is less fuel, so torque drops, we still need the same torque, so throttle is opened and ECU increases Fuel again. Now there is even less vacuum because throttle is opened and it also reduced whe EGR was enabled. Less Vacuum means less torque is taken sucking against the throttle plate, so consumption is improved.
BUT, in the combustion chamber you have more gas and less oxygen and fuel, so temperature is reduced, (causing less NOX) but efficiency is proportional to Tmax/Tmin (amoungst other things), so efficiency is reduced, consumption is increased!
the one fights the other, not sure which wins! Well, we know that with excess air consumption is reduced, so it will probably be the same, consumption will improve
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