It's probably not a good idea, but I see the thread rejects that there could be some balancing of the draw by taking current from both batteries. This would require 2 more wires isolating the negative, but a high drain item or two could be rewired direct with smallish wires so not too messy.
The charger would provide increased current even if only one battery is discharged, and the current is the same for both. In practice given how real world charging currents vary so rapidly with voltage this may mean you have more trouble with overcharging the unloaded battery than under charging the 12 volt loaded battery.