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Do you have any idea how WIDE the entrance to Charleston Harbor is?

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.

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.

You mean these chains? See: Link

There were two chains created and strung across the Hudson River in an effort to prevent the British from taking control of the Hudson thereby splitting the American colonies. The first chain, which weighed 35 tons and was 1650 yards long stretched between the base of Fort Montgomery and the rock at Anthony's Nose. That chain failed to stop the British forces when they attacked Forts Montgomery and Clinton. That chain was dismantled by the British.
The second chain was laid across the Hudson between Constitution Island and West Point. Each link was two feet long and weighed 180 pounds. This chain was never tested in its effectiveness against British ships. The focus of the war shifted to other battle grounds and they never again tried to bring their ships this far up the Hudson.

Here's more. Apparently nature played a role in the design of the Great Chain you talked about. A sharp bend in the Hudson slowed British ships down so they wouldn't have to momentum to been able to break the chain. From Link

The plan was for this sharp bend to slow down British war ships so that they couldn't break the second Great Chain, a chain of huge iron links on a floating boom of logs, which stretched from Constitution Island to West Point from 1778 to the end of the Revolutionary War. Trapped, the ships could then be destroyed by cannon. The chain was never put to the test, unlike the first Great Chain at Anthony's Nose. After their defeat at Saratoga, the British did not try the Highlands again.

I don't think the entrance to Charleston harbor had such a sharp bend that would have slowed Federal ships. And I'm not sure where the links of chain would have come from -- there were probably not too many large foundries in the South at that time, but I could be wrong.

Apparently the first chain on the Hudson was simply flanked and dismantled.