No, not required. Google Dalton's law in particular. It's all about 'partial pressure' : total pressure in a gas mix depends on its constituents and their relative partial pressures - a vastly complicated thing, simply/elegantly described
It's perhaps more familiar concept than it sounds:
A good example is the psychrometric chart - the amount of water vapour that air can actually carry varies wildly with temperature, even over the normal say 0-30degC we are used to. It's the foundation of air conditioning - cool air and the amount of water it carries drops markedly, the excess condenses out; now pass the air over the waste heat (warm refrigerant, in the condensor) and the air comes into the room at a regulated,similar temperature but with greatly reduced humidity. It's how you can get say 100kW of cooling capacity with only say 30kW of energy input. And then as a person in the room, thanks to the lower partial pressure of water vapour, you feel really cool even at 23degC, because sweat evaporates fast (with loss of latent heat) ... and none of this alters the other constituents of the air: we've messed with the water vapour content, but the % oxygen, argon, nitrogen and all other gaseous /vapour constituents are unaltered. You'd have to cool 'air' a *lot* more to alter those significantly.
Of course the ideal gas law is the 'rule', PV=nRT and all that: pressure x volume is a constant. So answer to first part of your question is... strictly yes, if your volume and pressure and temperature are very tightly constrained! I can't think when that might happen though, outside physics exam questions...
