Older converters are basically just constant voltage power supplies which can hold their rated voltage up to a certain load of amps. So say the converter puts out 12.6v 30a - then it will hold 12.6v at any load up to 30a - a load higher than 30a would start to pull the voltage down if the unit didn't overload and shut down.
Pretty similar to a regular old automotive battery charger. As long as the converter holds the bus voltage to 12.6v, then if the battery is below that voltage, it will slowly absorb power until it reaches equilibrium with the bus voltage. That's why they are often referred to as "converter/chargers".
So the converter not only supplies power to whatever 12v loads are connected, it also slowly recharges the battery up to 12.6v.
What you likely have is an old MagneTek power center. The 120v shore power comes in to it, and it passes that through to the 120v outlets in the camper. It also taps off the 120v to feed a built-in converter to supply 12v.
The problem with those old converters is that 12.6v isn't really enough for a modern battery. Most modern batteries need to be pushed up above 14v and held there a while to be truly fully charged. A smart charger will do that, and then once the battery stops absorbing power it will drop back to a "float" voltage, which these days is usually between 13.2v and 13.6v depending on the charger. The older converters were by no means smart.
The second problem, is that that old converter probably has a pretty low amperage rating. I.e., it might only supply 9a to the 12v bus and that's not much. The old Shumacher battery charger which is hard wired in to my camper puts out 12.8v and up to 10a and while it will eventually charge my battery up to 12.8v - it takes around 12 hours if the battery is really low.
That is why I'll be replacing it with a modern multi-stage charger. Not only will it still function to supply 15a to the bus for loads (I don't have many), but it will do a much better job of charging the battery and my generator run-time should be half what it is now.
If you add solar, then a decent solar charge controller, such a Morningstar Sunsaver, will be a multi-stage charger and will get the battery properly charged up to modern voltage specs.
IF there is enough watts of solar panel and IF there is good direct sun on the panel.
In that case, you could still use the ol' MagneTek if 9a (or whatever its rating is) is enough to supply your loads. It will only get the battery up to 12.6v, but the solar will override that when there is enough sun and push the battery the rest of the way up.
Current: 76 E-250, bubble-top, self-contained|couple of old Yamaha enduros
Previous wheelers: 41 Willys|78 FJ40|78 Bronco|84 Bronco|74 Ramcharger|78 Ramcharger|79 D150 PowerWagon|77 D100|79 D400 dually, converted to 4WD, utility bed, 10' Lance|75 Westy|69 Scout, RHD|bunch of others|bunch of bikes|couple of boats|couple of motorhomes|blah blah|so what|not my idea|just doin' what I'm told|wank wank|this space for rent|candy is dandy|but liquor is quicker