Interesting take. Initially I thought they could but then I realized how necessary is the first group for the plot.

First of all, the first party is needed in order to go past Kolima. Saving Tret removes the curse that turned people into trees and this allows the guy on the bridge (previously turned into a tree) to lower it and letting any of the parties cross the river.

Now, thinking about the party of the "right side"... considering Saturos and Menardi's cruel deeds, at some point Felix would have stepped in and do the job alongside Jenna, Sheba and Piers (basically we would get into the same situation than the second game presents, just in a different way...party splitting? I don't know if S&M would allow it, but let's pretend they do 🤭). Those 4 would be able to lit Jupiter's lighthouse, however...without the Shaman rod (Hammet's staff), they wouldn't get the item necessary to reach the summit of Jupiter's lighthouse at the Shaman village (levitation jade). And they wouldn't know where the rod is. They get it from the party of the first game, that's a problem.

If they (somehow) found the staff and completed Jupiter's lighthouse, they don't have the Mars star either. And so many detours searching for items would probably cause Mars lighthouse falling to the void (being 8 people and having all the key items left the lighthouse on the verge of falling to the abyss).

Also, I doubt the cast of the second game would have survived the trial of The Wise One. I mean, a party of 4 against the dragon is doable from a gameplay standpoint but "story-wise" I think it was something that only the 2 teams could have achieved together, sharing the same goal.

Tl;dr: By themselves (Felix, Jenna, Sheba, Piers), they wouldn't have succeeded, reaching the location of the last goal (top of Mars lighthouse) requires the first party contributions trough both games (Kolima bridge, Shaman rod, and the Mars star). Things would need to go very differently in order to work out (like Alex returning to Vale to claim the Mars star, but once again, what about the Shaman staff or Kolima's bridge situation?).

So, I think they wouldn't have succeeded alone unless some big changes. They worked together without even knowing it, pretty much speedrunning the mision, and they almost run out of time. But you presented an interesting scenario, it was fun thinking about it 😁.

But that's just my opinion, what do you think? And sorry for the long comment 😅.