Yes, your converter does charge your batteries. The best way to check if it's working is to measure the DC output, it should be between 13.2 and 13.8 VDC. The voltage should be fairly close to that at your batteries.
2007 Newmar DSDP 4023
Discovery is seeing what everyone else has seen and thinking what no one else has thought.
If you want to see what man made go East; if you want to see what God made go West.