as log as you have it connected correctly, with a reserve tank, it will expel the air on it’s own with the cap in place. It is common to fill the radiator and run the engine with the cap off until it cycles at least once, to get the bulk of the air out.
I have done so for brief periods, but never with under conditions other than “vehicle parked, hood up”. Sometimes it’s the only way to fill the system though, so it’s not automatically a bad thing.
I am with @jerv here. Parked, hood up. When the thermostat gets hot enough, the water will cycle through the engine, and you will see the water level drop. Quickly add water and cap it.
@Skaggfacemutt You can and it won’t… unless you open it while it’s hot. A cold engine has no pressure in the cooling system; a hot engine has around 15 psi. If you release the pressure slowly (and there are special caps to do that easily and safely, and a way to do it with a regular cap), you can even take the cap off of a hot system without being sprayed, but I don’t recommend it unless you know the trick; too dangerous for the untrained.