In theory, more head space means more alcohol, water, and light compounds (aromatics) can evaporate/diffuse out and mix with the argon. Argon does not diffuse into the wine as easily as oxygen or nitrogen so this limits the effect, but it is possible that a half bottle could lose some zest.
That said, I have not have that happen save for the one bottle mentioned above, but that was more oxidized than flat.
Volatile aromatics find an equilibrium between the liquid and gas, so the ratio can make a huge difference. Some wines don’t have much of that to begin with, like later picked (“riper”, “bigger”) wines, so won’t really change. Other wines depend on that sort of aromatic complexity and will seem flat if they’re lost. So, that’s one aspect. And, based on that, depending on one’s preferences, a person may see a very high success rate or an unacceptable failure rate.
Even people who do find a difference have worked out good strategies to utilize this devise, like sampling to a certain volume loss, then popping the cork and drinking the rest.