This has probably come up many times on some other sites I dunno but I guess I'll take a crack at it. As we know that Sean's story is most cannon in the storyline of PSIII, while others might be Arons. Well I'll go ahead and seperate these into seperate timelines with Sean being timeline A Crys being timeline B Adan being timeline C and Aron being timeline D.
We'll start with timeline D, Arons timeline. In the end he is thrown through a blackhole and meets the people of earth. There we understand that this timeline takes place and begins PSII many years later. So the theory of Aron and Ragol is slimly connected in timeline D. I will explain this later.
In timeline A: Seans timeline the team had just finished defeating Dark Force and continue to travel through space with the other worldship most likely not finding a new planet to settle on. So we can count timeline A out of this scenario.
The only two timelines that could connect into PSO would have to be Crys and Adans? But which one would connect you might ask. As we know for seperate timelines there are many possibilites of many things. Many versions of many things, such as you may exist as a top scientist in one timeline but may also be a street bum in another timeline. In fact I believe there are two Ragol's, each sharing similar fates with Dark Force/Falz. But we are only capable of seeing one timeline as we play through our quest.
We know in every timeline Dark Force/Falz is found randomly and is defeated by each of the heros in their respectable timelines. I believe that when Dark Force/Falz was defeated by the hero's it was actually trapped in the Orakio/Nei Sword. Now if we look at PSO for a moment there are three seals that must be unlocked before access into the ruins is acceptable. As this has been studied before the three seals are most likely similar to the three planets of Algo but I perfer not to go into this at this moment. Let us look back into Aron/PSII timeline real quick shall we.
Believing that in Arons timeline the Earthlings began working on the ship Noah after studying the technology of the Alisa III and learned of the original coordinates of Algo. While they were constructing the ship the darkness that was inside the Orakio/Nei sword began to slip out and finally took shape as Dark Force/Falz and began to destroy Earth. With the knowledge of Dark Force/Falz from Aron's memory that would be stored somewhere they would learn how to slightly defeat Dark Force/Falz, but only enough to seal it away. The struggle against Dark Force/Falz went on for many centuries I believe, eventually leading to its defeat and sealing. But at the cost of Earth being destroyed.
When PSII begins to conclude before the group fights Mother Brain they locate a chest. This is in fact the same chest that ancient Earthmen sealed Dark Force/Falz in centuries ago. Not caring what would happen to Algo they used it as a last means in hopes to destroy the solar system seeing as they went crazy. When PSII ends, we do not know if the Earthmen or if Rolf and group manage to survive. But in this timeline I believe that they may have won but in the end failed at the same time. With their last ounce of strength from the victory against the Earthmen they changed the coordinates of the ship Noah and it was launched through the universe and eventually found its way to Ragol. There the group would build a giant gravesite in the middle of a beautiful flower covered field and place a coffin with a magical seal on it with Dark Force/Falz's spirit sealed inside. Thus concludes Timeline D.
Now let us return to timeline B and C. Much like timeline D when Crys and Adan defeated Dark Force/Falz the spirit of it was sealed inside the Orakio/Nei Sword. After they learned that they would be approaching a star system and would make a new home. Knowing that there was a evil sealed inside the sword Crys and Adan would find the most dangerous planet, one that would most likely never be made livable by any Orakian/Layan. In the same solar system they would find Ragol, the most dangerous planet in the whole solar system and much like in timeline D they would construct a giant grave that would act as a amplifier that would keep the magical seal on the coffin as it kept Dark Force/Falz trapped in a prison forever.
As we can see in timeline D the sealing of Dark Force/Falz takes place back in AW 1284 (most likely a few decades later) So given that in timeline D the sealing would take place between AW 1284-1309 as a estimate. And in timeline B and C the sealing would take place in AW 2333. In anyway you look at it whether the sealing took place in any of these timelines at any years many many centuries later the seal would begin to weakin and the daughter of the principal of Pioneer 2 would be taken over by the evil that was Dark Force/Falz. Three seperate timelines, three seperate hero's, three seperate Ricos, all share the same fate. And this is my conclusion on the connection between Phantasy Star III and Phantasy Star Online.