There are many makes and models of converters.. The one you cited is, if I'm not mistaken, a 3-stage converter, this means that when it senses the batteries are full up, it backs off so it won't boil them dry, at least not fast.
On the other hand there is one I know of (And likely more I don't know by name) that is well known for doing what you fear.. But that is not the one you have.
Recommendation.. Check the fluid level in the batteries monthly. The proper is between the top of the plates and the bottom of the filler tube.
When topping off (WITH DISTILLED WATER ONLY) I like to fill to 1/8 to 1/4 inch BELOW the bottom of the filler tube or Split Ring as it's also called.
