If the Palmyrene realm can stabilize itself while Rome in the west reintegrates, I'd think they'd prevent or limit the Empire's shift of center of gravity eastward. OTL Constantine eventually established his new and major capital at Constantinople, but if much of the reason for his doing so were mooted because Rome did not control the rich eastern provinces anyway, perhaps either the capital remains at Rome itself, or at least a new one is established not so far east, so the defense against invasion more effectively covers the west as well.
Bottom line--by pre-emptively splitting off a crucial part of the OTL Eastern Empire, might the division of the rest of the Empire be prevented?
Frankly I doubt it because first of all the Romans would be pretty obsessed with reconquering Palmyra, and unless the Palmyrines were able to actually seize control of Antatolia and central Greece as well, I suspect that "Rome" would have shifted East just as inexorably as OTL; after all capitals were often moved as much to present a strong front in wartime (with Emperors mainly preoccupied with waging the war, they needed to be resident near the front) as to occupy the center of the source of wealth. Worse, I suppose that by the time the Empire split and left the Western Empire to rot, the Imperial society as a whole was losing both means and will to defend the western reaches; trying to force the center of gravity west might or might not cause a reevaluation of what was vital, but might by no means provide any more resources to try harder with!