When the solenoid is active it causes the timing to advance, all this has nothing to do with the check valve in the fitting and only effects emmisions, Stanadyne IPs before emission controls did not have the cold advance feature and none of the off road (tractor) IPs have this feature.
But if the pressure rises to the same as the charge pump (completely blocked return) then the plungers will not be able to take in any fuel and the engine will die, the differential in pressure between the charge pump and the housing is what forces fuel into the plungers.
The check valve ensures that the proper pressure is maintained in the housing so you should replace that fitting, although I have run several IPs with that ball removed over the years with no obvious detriment although another job of that check valve is to ensure the fuel does not bleed back to the tank causing a fuel starvation upon startup.
Here is an explanation of the Stanadyne cold advance system.
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