That would be very weird if that was true. Unless the amount is so low like a nickel a drink, that it doesn't influence the servers' behavior.
On my last cruise, I became a regular with several of the bartenders. With a couple of exceptions, they didn't even bother to enter my drinks after I became their regular (as seen on the app). Knowing that it wouldn't cost me anything, they would have entered the drinks if it would result in financial benefit to them.