Running the watermaker underway will mean running the generator underway. Unlike the saildrives, the generator intake is not typically as deep and more easily takes in air or seaweed. We never run the genset underway, though people of course do and get away with it. Officially (Moorings) you're not supposed to.
Depending on circumstances, changing the filters might be preferable to waiting for the chase boat to come out, it's nice to have the option. Moorings usually puts spare filters aboard. They certainly will if I ask.
It's my understanding that if a watermaker isn't used for 2 weeks, it should be "pickled". I doubt this is consistently done. Also, after stopping the watermaking process, there is supposed to be a flush (backwash?) cycle, but there's nothing to prevent the user from just turning off the breaker and bypassing this step, which I'm sure increases problems.
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