The other day I took my 98 yukon in for yearly inspection. Ha, it failed because of a diagnostic code. The code that came up was p0446, which is evaporative emission control system vent control circuit. Will pumping gas while the vehicle is running cause this code to be present?

Definitely. So will a gas cap that is not put on or a gas cap gasket.

The other day i took my 98 yukon in for yearly inspection. Ha, it failed because of a diagnostic code. The code that came up was p0446, which is evaporative emission control system vent control circuit. Will pumping gas while the vehicle is running cause this code to be present?

Probably not.
Why not?
Because the parameters neccassary to run that diagnostic test require that engine coolant temperature (ECT) be between 4-30°C (39-86°F). Your ECT should be much higher than that, even if you're less than a block away from the gas station when you started your cold engine.

The MIL will turn OFF after one ignition cycle in which the diagnostic runs without a fault.
The Freeze Frame information and the history DTC will clear after one ignition cycle in which the diagnostic runs without a fault.
If your DTC is "hanging around," the problem is more likely a bad gas cap seal or something else in the evap system has failed.

OK there were three MIL checks done:
Engine off MIL check - passed
Engine running MIL check _ passed
Commanded MIL - failed

The vehicle passed visual, safety, and gas cap inspection but failed obd2 with the resulting p0446 code. I had the code cleared have it checked again possibly Monday. I am leaning towards it being that the canister and solenoid may need to be changed, but I will see then.