For this years chem question? No it doesn’t unless Gay lussac’s applies
In Chemistry, Gay-Lussac's Law concerns the volume ratios in which reactions occur at constant pressure and temperature. There is no reaction occurring involving argon, so this law is irrelevant.
Physics books sometimes describe a pressure / temperature relationship as Gay-Lussac's law, which is also sometimes called Ammontons' Law. Gay-Lussac's research in this area was actually looking at volume and supports what is called Charles' Law in Chemistry.
Even if the pressure varies in direct proportion to absolute temperature law is what is meant y Gay-Lussac's Law in above posts, it is not applicable to this system as it reflects pressure changes for a given sample of gas at constant volume,; as such, it requires a constant gas sample in terms of moles of gas / number of gaseous molecules. The pressure increase here follows directly from the added argon, so the gas composition is changed and the conditions for applying the law are not met. The Ideal Gas Law Model makes this clear, in that a k% increase in moles results in a k% increase in pressure when volume and temperature are unchanged.
I can't see any way for even the Physics version of Gay-Lussac's Law apply.