Function update!!! I did some investigating and found, on my 2018 210 FSH anyway, that the bilge pump is indeed wired directly to the battery, and does indeed have a float switch.
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Battery switches both off.
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Bilge switch also off. In this configuration the switch will not initiate the pump manually.
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Filling the bilge with a hose however, once the water reaches the round blue tabs that hold the pump to the screen base, pump will kick on whether the battery switches are off or on.
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When the pump turns on, the switch indicator lights up to show the bilge pump is running. To note, the switch will not run the bilge in manual mode without the house battery on. I also noticed it took a really, really, long time running the hose to get enough water to run the bilge. Like, 5 minutes running full blast. This information will be useful, and is also OPPOSITE of what the manual tells you on a 2018. My dealer was correct after all. In conclusion, it seems as though the 2018 and later have a more sensible bilge pump setup, but I would verify this for yourself before betting your boat (or life for that matter) on it.