i dont think so chengis was smart enough that he knew that chosing juchi or chagatai would lead to problems so he chose ogedie and the first born dying before him helped
even if juchi had lived i think he would have respected ogedie position, even if we kill of ogedie there is still Tolui .
the only scenario can think of is that ogedie dies shortly after his father and the supporters of tolui would want to make him khan but for some x reason juchi says he wants to be and chagatia disagrees and reject the election of tolui since no one would elect chagatia or tolui
but even then juchi was already allinated and his father had already taken him away from the succesion any power grab would be met by tolui and especially chagatai so even then i dont think it would collapse.