That the war would have happened if Lincoln had not sent the supplies to Fort Sumter?

Yes, I think the war would still have happened because there were many issues other than that. For example, the South still wanted slaves and were already wanting to break away from the abolitionists. Also, there were economic differences between the North and the South. The South had crops and cotton fields and they needed saves, but the North had factories and machines and businesses so therefore they did not need slaves. There were still many other problems and disagreements and there was bound to be a war anyway. The attack of Fort Sumter was just one of the main causes.