Disconnect.......
No, I do disconnect them from my electrical system. I usually just disconnect the ground.
If you want to leave the battery in place and charge from the boat, then you should buy a battery isolation switch. You can buy them from Walmart (in season) or any marine supply store.
You always need to isolate the electrical system before charging. And if charging in the boat, always maintain proper ventilation. During the charging process, batteries create hydrogen gas through sulfuric acid (battery acid). That is why you see the little vent tube on the battery, connected to the outside...........no vapor build up in the engine compartment while the ski is running and charging the battery.............:cheers: