I purchased a 2006 Airstream used in 2009. Airstream put a crummy single stage converter/charger in their trailers back then. Yeah, a big expensive trailer with a crummy charger. Go figure.
The PO left the trailer ALWAYS plugged in. When he went out on location he always plugged it in. We showed up to check everything and it was plugged in. Everything worked and there was no smell from the battery compartment.
After we got it home we found out it wouldn't hold a charge. The batteries, both of them, had been toasted. We replaced the charger with a newer three stage charger and everything is fine now.
Yes, your batteries can be damaged so get them checked. But, my guess is that your charger is not working or that it is a single stage charger so it IS working and boiling your batteries.
Let us know what you find.