Sure they can. Let me give you an example of what they can, and probably will, do.
Yu Narukami's story is almost certainly going to have actually happened. He'll have won the tournament, saved Labrys, etcetera. However, the events in the other character's stories will have happened as well. Naoto will still have delivered her report on Mitsuru and the Shadow Operatives. Even though, if we do take Yu's as the "official" path, Naoto would have lost earlier, been stuck sitting in one place, and never have gotten the interaction with Mitsuru that wound up driving the conclusions in her report. Chie is still going to look up to Akihiko as a mentor and guide. Even though, again, unless she actually was the champion in the tournament, she would not have had enough interaction with Akihiko to form that relationship. All of the events of the story will have happened, even though the events do contradict each other.
Also, your point wasn't that there was a single timeline that ATLUS was following, but rather that anything that wasn't being directly carried over or expanded upon in later games wasn't worth playing. That because in Persona 4 Arena and Persona Q, the main character of Persona 3 is male, the female main character story doesn't count. Similarly, I guess, Marie's story in Persona 4 Golden doesn't matter, since she wasn't mentioned, nor were any of the events in her story. I guess we can assume that Yu didn't max the Social Links with any of the Investigation Team, since none of them had their final Personas in Persona 4 Arena (even Teddy, who you have to max to beat the game). I guess that Yu didn't romance anyone, since there is no romantic indications given in any of his interactions in Persona 4 Arena. I guess you should just play Persona 4 without forming Social Links with any of your team, without getting a girlfriend, without exploring any of Persona 4 Golden's extra content. And I guess you can't really play Persona 4 Arena at all, since all the stories contradict each other and you can't find a single timeline in there to follow.




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