It would have made no difference. Davis would have used force to prevent any resupply effort. All he had to do was prevent resupply for a few days and Sumter would have surrendered. If he allowed to be resupplied, he would have a political firestorm on his hands.
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.