That is correct no charge regulator, constant charge rate of 2 - 5 amps, depending on what you have it set for.
The disable switch (either a switch or a jumper depending on your board) to turn off the battery charging circuit is on the regulator board inside the electronics box. You can access it by removing the lid on the electronics box. I don't have my personal Onan manual here at home to tell you which switch. Maybe someone else has their book at hand and can give you the switch/jumper number. As others have said, your boats smart charger will do a better job of keeping your Genset battery charged and not over charged.
PS: I have the Flight Systems aftermarket electronics board in my unit. Yes, it's better quality and moisture proof, but doesn't solve the charging issue you are having.
Here is a link to an online Onan MDJE manual, but I don't think it covers the electronics box. Check it out though.