Does this actually minimize fuel consumption?

In your mind yes but technically NO, the rate of fuel consumption for an internal combustion engine (ICE) is decided at the carburetor or injector under the guidance of the throttle allowance . This valve you have shown is just in place to starve the carburetor of fuel and once your engine is running smooth it's means the carburetor has enough fuel

Not at all ...the fuel would still collet at the injector and pump in at normal rate

Reduce load if I want to save fuel

To me it does reduce fuel consumption but to detriment of carburator.
But caburator isn't that expensive and will take like 5 months to spoil.
I do it on my gen, it usually takes me 14hrs for full tank but halving the fuel supply extends it further 4 to 6 hrs.

I on the gen 6pm last night and it's still on, and would be till around 1.
What it does is reduce thw flow of fuel that should be burnt.

Am here to also learn