If those ships hadn't shown up, that is exactly what would have happened. Of course, as Kalamata has pointed out, Lincoln said he would retake any forts, so it wouldn't have mattered. Lincoln was going to have his war one way or the other.
If he allowed to be resupplied, he would have a political firestorm on his hands.
And if Lincoln couldn't stop the South from trading directly with Europe, he was going to have a political firestorm on his hands too. Too much money would have been lost by powerful people in the North, and they were not going to let that happen.
If those ships hadn’t shown up, that is exactly what would have happened.
That is correct, no resupply, Sumter surrenders in a couple of day.
An unarmed merchant ship, showing up with provisions for the Fort would have caused Davis to Fire on the Fort. He was not going to allow provisions to be landed by anyone.