Opening the gas cap whith the engine running will not adversely affect anything. The fuel system is always under pressure (not vacuum) between the fuel pump and the injectors. The gas tank is outside the pressure circuit.
Most cars yes, I do that all the time with my other cars…..but the Armada no. Try leaving your gas cap open and turn on your car...unless you have a tuning software you'll be making a trip to your dealer to have them turn off your check engine light.
I was told this by the sales person and one of the mechanics at Nissan when I wanted to swap out my gas cap for one with a lock.
They told me the whole pressurized vacuum thing the Armada/Titans use and how they have had a lot of problems with people swapping out their caps for the keyed ones that don't seal as well. And because they don’t' seal it causes issues with the fuel relay setup and throwing the check engine light.
I didn't care enough to go research it and find out how it really works, but I also don't feel like using my car as a guinea pig to find out. If you would like to try it, be my guest and let me know if they are right or wrong.