I have to dispute your idea. Do you have any idea how WIDE the entrance to Charleston Harbor is? NO WAY would they have been able to block entrance to the harbor. I know from personal experience on this one. I was in the Navy, and my sub passed that way everytime we went out to sea.
About a mile, although the ship channel was much narrower. Still, given that in 1778, the Americans were able to put together the 1500-foot "Great Chain" across the Hudson at West Point in just six weeks, I still contend that a passive barrier across the harbor mouth would have stopped resupply for a couple of days until Anderson surrendered peacefully. But as I said above, firing on Sumter worked to the southern advantage too, by forcing Lincoln to respond militarily, which in turn forced the upper south to join the lower south in secession.