This is a docs bug. The docs say you must set it during init, but you can actually set this property at anytime during the Interactive phase of the web data connector. For example, I took the IncrementalExtractConnector from the WDC SDK samples and moved the line that sets the columnId out of init. The connector still worked fine.
Let me know if that doesn't work for you. I'll follow up with the team here to get the docs fixed, thanks for reporting!
And yes, you are correct that if you do not set this attribute, all refreshes will be full refreshes. With the column set, you are given the choice between a full and an incremental refresh when you go to refresh the data source.