While the sea might be deep all those undersea cables come ashore at some point and satellite links would not be able to take the load if a bunch of cables got cut. However, domestically as consumers we probably would not notice a total blackout, but information and connectivity to/from overseas would be painfully slow or nonexistant.

If China converted all their civilian merchant ships currently sitting off our shores into military ships overnight we would be blockaded. I'd be more worried about that.