No, not impossible. When the port is closed, it is usually only closed to boats of a particular size (i.e. boats that take out divers/snorkellers). The ferries seldom stop running as they are CONSIDERABLY larger and more stable. So yes, when there is no diving on the island, you can grab a ferry to the mainland and go to the cenotes.
Several suggest to stay in Cozumel and only go to mainland if a norte comes and go to cenotes. But if cozumel port is closed this will be impossible. Am I to read these suggestions as a way to deal with a norte that doesn't close the port but is bad enough that there is no diving on the island?