If he was hoping to provoke a war then why would he make it clear that had the South not intervened then only food and supplies would be landed? Wouldn't he have just thrown men and munitions in along with the supplies if his intent was to provoke a war? By clearly differentiating one from the other it looks more like the act of a man who is leaving the question of peace or war in the hands of Jefferson Davis.
Sumter was short of food, that is indisputable. The confederate intent was to starve it into surrender and change the balance. Lincoln's intent was to maintain the status quo. Which is more peaceful?
You trust a president that had just flip-flopped about evacuating the fort and tried to sucker South Carolina by sending an unsigned letter claiming he would only send in supplies?