It SHOULD NOT matter...meaning we have smart chargers, so if they sense a full charge, i.e. from the Alternator all should be well.
HOWEVER, since I am a bit OCD, I do turn off the Battery Charger while underway...and then when I get to that cove and power off the engines, I turn it back on. But once again, I think I am just overkilling in...
Others will chime in as a few folks have a ton of electrical knowledge.
I wouldn't think it should matter either.......I agree that our chargers and alternators should live together in harmony under normal conditions.......not so sure if you developed a dead cell or short within the battery though...? Things maybe could get a little funny then ???
I would also think it shouldn't matter, I would think they are "wired" to live together. Having said that there is no reason to run both and would probably turn of the battery charger at the panel when under way and running the generator.