No, Uchiha and Senju feud could have only happened if either :
1. Indra's offspring was/were old enough to know Ashura killed him
2. or if he/they inherited Indra's will to kill Ashura's lineage and gain power
In either case they would have to be AT LEAST over age of 6 because children under that age generally have no conscious memory of their childhood and parents (as proven by Sarada) and therefore have no reason to fight like their parents.
The feud was definitely started by Indra's side though because Ashura wanted peace and wouldn't have told his offspring to kill his borhter's descendants.
The way I see it, Indra and Ashura died when their children were old enough to be aware of what was happening between their fathers and Indra's child/children decided to avenge him while Ashura's descendants were simply defending themselves.
In addition, Hagoromo's death and the death of his sons led to a power vacuum which allowed other clans to join in on the conflict between Otsutsuki descendants, that eventually resulted in the era of clan wars
